Yea in this case I'd also suggest to just insulate it. Try using insulation tape. It's pretty thin and should do the trick. I'm not sure how it would be called in you country but the stuff usually comes in red, blue, and brown greenish colour, is rubbery and stretchy.
However i'm not sure what the best way to apply it would be. Since putting the tape all around the metal part might make it too hot?
If you have a hot glue gun (also not sure how you call...