+1 for the paracord fish method.
When disassembling the buttons from the housing, I suggest that you take photos of it before you remove stuff. It goes together pretty logically, but it's nice to have a reference to look back to. Now would be a good time to grind off the "nub" that forces the housing to be indexed at a certain position on the handlebar, presuming that you want to do that and haven't already. If you aren't going to rotate the housing, move it in/out, or use aftermarket bars, then I guess skip the nub removal. If any/all of that is "already knew that" stuff, then ok, but if not, there ya go.