Tomorrow I plan to stick a humbucker from my broken Epi Les Paul into a cheap Strat to see how it sounds. Because it's just a test, I'm just going to wire the pickup (in the bridge position) to the input jack.

The pickup only has one wire coming off it, so can I just solder that wire to any part of that jack? (Not literally any part, obviously)

Would I need to ground the circuit from the other part of the input jack to the tremolo cavity?