Afraid I'm not a diver or snorkeller so can't really give you any pointers on that. You do see a lot of people who lug gear during walk ins though.
The one thing I do know is that not too long a go a cave with some of the best prehistoric paintings in Europe was discovered right at the bottom of a crag at Morgiou... 40 below the water. Website below (in frog unfortuately).
Re Chamonix...I picked up the just released guidebook for the Aiguille Rouges (range opposite Mont Blanc) while I was there last week. If you packed your trad gear there's some great looking routes on offer. Do you want to get hold of this? You could drop it back when you're in town.