When we go to an amusement part, we have the philosophy that if it rains, "every ride's a water ride!". We all learned a long time ago that we don't melt.
It rained when we were in Grand Cayman - first while we were snorkeling: it felt like someone was tickling my back and it looked really neat hitting the water. Later while we were walking around in the town - after first trying to leap between overhangs, kids and I looked at each other and said "every ride's a water ride!" and just enjoyed it.
If you really must, take one of those 99 cent folded up rain covers that you throw away after one use.