The ship is easy, use a Bulk Carrier
Unlike a container ships, bulk carriers have several (typically 5-7) giant hatches for storing large amounts of unpackaged goods like ore, grain, coal, lumber, etc. Some larger bulk carriers will be deep enough to fit a road capable ICBM launcher into, and wide enough to pack in a few hundred. Unlike a heavy-lift ship, these bays will keep your payload launch ready and concealed. Just open the hatches and start firing to your heart's content... but there is a major problem...
Getting it loaded is not so easy
The tricky part is the size of ICBMs. Even a road capable ICBM is on average 21-23m long and 45-50 tons. Most harbors can not handle bulk carriers with a 21+ meter deep bay, nor do they have cranes that can lift 45-50 tons. Furthermore, most of the Bulk carriers in the weight class seem to cost a bit over \$100 million which means even if you found one on discount, it would not leave any funds left over for retrofitting and operations. So, you'd be limited to a hand full of very major ports that you could use to load your missile ship. This is a huge problem for your supervillain because loading and unloading missiles at such a major port is not going to be able to be done in secrete, and building your own port on this budget at this size is not an option... besides, any port this size will attract a lot of government oversight even if your could afford to build your own.
Use strategic nukes instead
There is no reason to put an ICBM on a ship, the whole point of an ICBM is that it can be launched from anywhere, to anywhere in the world, but cargo ships can cover most of that distance themselves. If your villain has road capable ICBMs, then it makes more since to simply park them in some woods or something where satellites cant see them.
Instead you could use a shorter ranged cruise missile. There are modern cruise missle in the 7-10m length, 2-3 ton range that can fire nukes 2500-4500km. Such a weapon system can threaten an entire nation or group of smaller nations... but more importantly, they will fit into practically any bulk carrier and are light enough to be loaded by any port crane meaning that it is much easier to find some unscrupulous dictator or cartel warlord who will let you use a smaller port off the beaten path to load up your missle ship.
If your goal is to threaten many countries over a larger area, 2-3 smaller bulk carriers would be in your budget... technically you could afford 4, but you'd have to plan on spending a fair amount on turning those bulk bays into proper missile silos to keep your first launch for causing a chain reaction blowing up your ship.