Connect how? I think you'll find the amount of current needed to heat a, what is this anyway, tin plated steel shield? is rather incredible compared to the item and its size. Like, over a hundred amps. Plus the shield is connected to board ground which will see some current draw and voltage drop, maybe not enough to cause problems but it's a weird concern to have in the first place.
Induction heating might be something as well, but the risk of inducing voltage directly into signal traces is even higher. (This is however the standard method for opening hermetically sealed enclosures, like for avionics.)
Anyway, there's nothing wrong with plain old hot air reflow soldering. If you're having trouble like, bumping other components, perhaps try covering them with polyimide film or tape (be careful with tape, as it'll be under tension and may shift, making everything much worse of course), or consider getting some tooling to simplify the action (some kind of grasping and lifting jig?). Or, consider using a preheater so that the hot air machine has less work to do, maybe possibly able to get more localized heat that way?
Tim