It gives me sweaty palms too. I wonder why that particular physical reaction happens, surely sweaty palms is the opposite of what you want?
I will note also that compared to climbing rocks, climbing trees with slightly sweaty hands is MUCH easier than with dry or chalked hands. I think its due to bark being the grip target versus rocks.
Nothing more than my experience but sending a cliff is nothing like climbing trees.
The strategy involved in the two is night and day. One focuses on fingertips not slipping and the other involves not losing grip.
In fact there's a high level climber who's sweat glands do not work and to compensate he has to bring a water mister around with him so that he can climb.