Both Premiere and AfterFX (Adobe software) can be used for green-screening & chroma-keying. Likely Vegas does as well, but since I don't have that, can't say for sure. It's a fairly straightforward procedure.
Wire Removal - I bought some software called "Commotion" a few years back that could do that. I never used it... but it could do it. 8) It was kinda pricey (at the time) but I am sure there is something better available now.
If you're doing the "complicated camera movements" you'll be wanting to look for software that has decent motion-tracking with it... however, you mention it is also stop-motion...
The wires will be supporting a very lightweight puppet/model of some kind? If so, the wires required would be really thin, like fishing nylon. You could fake zipping up the thin line by using the "Clone" tool in Photoshop, frame by frame. Rotoscoping takes a while... but so does stop-motion, anyway.