Aren't most of the Rickenbacker 300 series maple? It's been a hot minute since I've had one (360, I think, but the nut width was too narrow for me), but I vaguely recall it being maple. It was a semi-hollow, though, so FWIW and all.
I'd finish before shielding. If you're rocking single-coils it may be worth it to shield pickup cavities (I would as a matter of course), but make sure they're all connected to ground or it's not worth the effort. As to shielding the passages, just use shielded wire and be sure the shield is connected to ground somewhere (but only one somewhere, because ground loops and yadda yadda).
Updating to say that from my experience maple doesn't take stain very well/consistently, but there are probably pre-stains/conditioners out there that help mitigate the issue. If you're looking to do a translucent colored finish you should look into tinted lacquers or that sort of thing. Or just stain it anyway. It'll probably look sweet regardless.