Here are a few issues I see with underwater shaving:

1. I sure wouldn't want something as sharp as a straight razor right next to my regulator hoses! Unless you're planning on taking the regulator out of your mouth while shaving (and maybe putting it back between strokes), you're going to have to shave around the regulator's hose line. The one advantage here is that the mouthpiece has the effect of pushing your cheeks/lips out a little, so maybe this will help with skin stretching!

2. If you nick yourself, it won't just sting in the salt water, but will also attract sharks. But - at least you'll have a straight razor to defend yourself with.

3. You have a facemask on - looking to the sides or down will be very difficult. Therefore it will be hard to see where you're actually shaving. Possible advantage though - most dive masks cause everything to appear magnified in the water. So maybe when you look into the mirror (that your dive buddy is presumably holding) everything will look bigger and therefore it will be easier to shave.

4. Some people say barracuda are attracted to shiny objects - I hope you don't have a polished blade!

Goodluck with the experiment!!