On the Laser, my friend used to strap his countdown watch (Heuer) around the mast or boom. I cannot remember which, but the next time I see him I will ask. The boom on the Sunfish is thinner, but I don't see why that wouldn't work on the Sunfish. The mast would be my choice, since it is forward and can be seen on both tacks. Not sure what the rules would say, but my guess is that they would object. Wrapping it around the hiking strap might be ok, but that's low in the boat. You could also tape / velcro it to the splash rail. Any digital countdown watch would work as a Heuer watch is ridiculously expensive on eBay.
I know from my own experience that one's wrist is a bad place to have the timer. You have to look down and back exactly (when on Starboard as you approach the line) when you should have your head up and be looking forward and around you.