Condoms
It is best to check in real life what kind of options we already have. Condoms might try to protect for different reasons, disease and pregnancy, but their goal is to separate two 'objects' from each other, including any liquids or other stuff containing disease.
We can try to apply this to an elephant. It can roll down a condom, which I'll further refer to as a plastic glove, over the trunk on the outside. The inside can be tricky. The glove has 2 long plastic flexible tubes attached, good for each nose. These can be sucked in by the elephant, creating a sort of laminated inside, protected like a condom would do.
If the glove has sealed ends it has to be sucked in together with whatever needs to be handled. The elephant knows the limit, as when it reaches the full extent of the glove the resistance to further sucking spikes. As it can breathe through the mouth it should have no problem moving it to a different location. It can then blow the contents when needed. The glove can get folds and be difficult to suck in when doing this. That increases the chance of breakage, but depending on the safety thickness we can make very safe options. I understand (similar to) condoms are used in survival kits on open seas, as they can expend to many times the size with little chance of breaking. This way they can hold sea water that'll be treated to be drinkable (never had the chance to fact check this though).
An alternative for less dangerous stuff is an open end. This way the elephant can smell it and inhale at least some of the contents. On the end can be a filter or even just tiny holes for extra safety. I assume an elephant feels until where it sucked the contents and can stop before it reaches the hole. That way it is easier to suck stuff in and blow it out, as the glove can stay fixed in the trunk.
Gloves and condoms can give plenty of fine touch sensation if high quality. Though cheaper gloves like some heavy duty ones I have for cleaning can still function great when handling stuff. Even though it's very clunky.
Though with much more dangerous materials we can also go the smart way. In many hazardous materials labs we use machines, mechanical arms or even something as simple as a trolley or a drum to move these materials. A smart elephant wouldn't come close to these materials.