It can be done, however, you will probably have trouble finding someone to do it. Your best bet is to get an old aquarium, the right drill bit, and practice on it until you are confident enough to do it yourself.... then be ready for the worst, just incase something goes wrong.
I drilled my 210 glass aquarium full of coral and fish. Superman helped me out with a nifty drill guide and diamond bit. We just lowered the water level, set up water irrigation for the drill bit (bucket of water/ powerhead and hose) and went at it. I would have buckets on hand in case of disaster however.
IMO: A 75g tank is not large enough to take the risk. While it is more work than trying to drill with fish/corals. It is not that big of ordeal to just move things into a temp setup/bins ( basically anything that can hold water ) and drill then reassemble. Can easily be done in a day. Or maybe even better to just get another 75g have it drilled, do the swap, then sell/trade your old one....That way it the new one breaks you don't have stuff in holding tanks.