One major factor that is particularly out of place, here: "The Modern Age". Typically, elves are depicted as an ancient race. One that has been around a lot longer than we humans; sometimes since the dawn of creation. While they are not traditionally seen as a race that would live through to the modern ages 1, this does put a particularly interesting spin on things: they have been around to endure and overcome their potential weaknesses long enough to permit the inclusion of great time-spanning solutions.
I can think of several ways they may evolve into the modern age, to adapt to the increased proximity to corrosive metals. I can think of many ways these would adapt into their own paths, telling the story of how the elves overcome this natural weakness. Ultimately, my solutions boil down to three things:
- How far have the elves evolved, from their early "folk-lore" days to the modern age?
- How have they developed, magically? Elves are commonly seen as magically gifted - but this usually correlates with their great age in comparison to the other races. As greater time moves on, has their magic dwindled, or grown stronger?
- How are their relations with the other races? Do they still live more isolated communities, or are they more likely to go for a walk and run into a human driving a car? Likewise, do these relations offer economic advantage? This seems like an important issue that would effect trade values and such.
Following a Darwinism approach, it is entirely possible that the elves may evolve to adapt to their great weakness. Especially as the world around them changes so dramatically. Traditionally, elves would live in the forests, and often be seen as a nomadic race. However, as time goes on, many other races would rise, and perhaps fall. As other races advanced in technology, it is entirely plausible that the elves would have much greater interaction with iron, though not to the extend where they would have dangerous interaction with it.
As more structures are erected around the world, of steel and iron, the elves would have far greater interaction with the metals without coming into physical contact with them. That is, they might walk past an iron statue every day, without actually touching it and risking harm.
As years turn into decades turn into centuries turn into millennia, the elves might find that the greater increase in "close proximity" has led to them evolving away from their natural weakness. This might not necessarily be a matter of being able to work with said materials as commonly as other, but it is plausible that they could have far greater interaction before succumbing to the harm that was often suffered by their ancestors.
Greater natural protection
An option that provides greater creative license in your physical depiction of these elves is that of evolving natural protection. Perhaps their skin grows hard and course to limit the effects of physical interaction with the metals. Perhaps they move in the opposite direction, and develop glands that secrete lubrication over the key areas (hands if they particularly craft with the metal, full body if they rely on body armor) that acts as an extra barrier.
It is plausible that through having to adapt to the use of such metals, particular families have evolved towards greater resistance, while others have not. This could potentially lead to a 'caste' system of sorts. The elves that develop resistance might be 'pushed' towards career in smithing, or other jobs that require greater interaction with the metal. Elves that fail to develop the resistance would be more suited for other occupation, such as general farming, or mage work.
With all the advancements we have made in medicine, it is not a far stretch to suggest that elf-kin would reach far greater advancement. A natural affinity for nature mixed with the greatly extended life span makes for excellent medical study.
Over time, their advancements could allow them to develop remedies to their weakness. This might be something as simple as a common salve they could rub into their skin to provide resistance against harm, or even a remedy for those that are around the material so much as to develop serious condition.
If you think about all the seemingly insignificant ailments we suffer that would have been an easy death sentence hundreds of years ago, its not hard to reach the conclusion that the "iron weakness" could be the elfish equivalent of smallpox, or scurvy. Both of these ailments were once considered fatal to humans. Smallpox was effectively wiped out through the spread of a less fatal 'little sister virus' (cowpox) that prepared our immune systems, while scurvy was eventually correlated to the lack of fresh fruit and vegetables in ones diet. It does not seem completely unreasonable that the elves may come upon a similar solution to their own problem.
Just as humans have extended our reaches through advancements in technology, it is entirely expected that elves would make advancements throughout their many years, magically. This gives you all sorts of possibilities.
With greater developments in magic, elves could learn to harness nature to create far greater barriers. You might go for the "runic ward" approach, where more powerful runes can be inscribed into iron garments to nullify the effect (by blocking it, or even by providing a healing effect strong enough to cancel out the harmful effect). You might even consider the use of delicate magical barriers to physically prevent the elves from touching the metal, while still having enough motor capability to interact with it. Think something a long the lines of capturing wind into a fine glove, that provides enough barrier to allow you to pick up things without actually touching them.
Greater reinforcement of safe material
With the use of powerful nature magic, you could allow your elves to develop knowledge for reinforcing natural materials to compete against our modern metals. Magically infused wood or glass could theoretically compete with steel or iron, depending on the manner in which they do so. It might be more feasible to suggest the discovery of more advanced variations of said material. Perhaps they discover a particular tree that is so strong that only the will of nature magic itself can allow them to fell it, and use it in craft.
Greater advancements in refining safe material
If the elves have to use metal, ultimately they are going to use metal that is safe to touch (in most cases). As mentioned, they can touch titanium. Titanium is somewhat uncommon, when compared to steel, but this partially boils down to the fact that it is still very difficult to actually make titanium. From what little I could find at 2 o'clock in the morning, this is mostly due to the fact that the creation process requires great amounts of heat and pressure. Surely if the elf's pushed for advancements in their magical abilities that greatly accelerated their ability to create titanium, this would easily be a more suitable alternative to steel or iron - even without the weakness.
Building on another answer, this might make them particularly useful to the dwarfs. The dwarfs might have their great machines, but they are not known for their magical ability. With the elves providing them a steady source of "magically-developed titanium", they would surely be inclined to offer the services mentioned in other answers that would make these metals less dangerous to the elves - whether that be diluting the dangerous metal down into less dangerous sub metals, providing other metals that might be out of reach to the elves but otherwise safe, or even through providing the required electroplating needed to make general steel or iron completely safe for elf-kin to interact with.
1 Not including science-fiction re-imaginings of the race, of course.