stitches - no prob.
The day of the Belmar Pro I was surfing down in Spring lake and my board hit me right in the face when I was under in the backwash. Right on the bone under my eye -- I took 29 stitches to sew it up. two hours later I was back in the water, I covered it with several layers of "liquid bandage." Sometimes called Newskin . . . it's basically a watered down cyanoacrilate, it hold things together and keeps water out. I was fine. The problem with your hand is that you keep flexing it, I guess. I had no problems surfing and the scar healed up great.
I too agree with using a Liquid Bandage. For extra precaution use a latex glove or 2 taped up.
You are going to be more susceptible to re-injuring your hand, and this will slow the healing time WAY down. The choice is yours, but I'd stay out of the water for awhile if you want it to heal as fast as possible. Re-injuring your hand will just prolong the healing process. Sucks to hear, I know, but it's worth the temporary time-out.