A good Polar strap propertly wetted under the cold water tap works fine straight out the door. The only time I get problems are if its very cold and windy and it dries out or I bend down (say to tie shoelaces, so always put trainers on first). Don't wait for it to work off sweat.
If anything your race/training differential is quite small. Do most of your training at a pace where you could/can hold a conversation. In the race you should be breathing very hard, just on the edge of blowing up.