One thing that players of plastic recorders do is put a diluted solution of washing up liquid down the mouthpiece. I have tried this and it works very well with recorders. I have never needed to do it with whistles, though, and don't know if it would work as well.

You could try warming up the whistle prior to playing. Stick it under your armpit for a few minutes, also blow hard down it to raise temperature. Both help with condensation in my experience.