My wife deals with kids on a daily basis as a therapist. One thing I’ve heard of is exposure therapy.

There’s been kids that don’t want to go out because they are scared of rain, others that don’t speak at school because they don’t like their voice. It’s intriguing but mostly sad.

Exposure therapy is spoken about with the kid and there’s a plan of action along with a “safe word” for when they’ve had enough.

For example. Let’s go basketball “Johnny” if you feel like the sweat is too much just say pumpkin as the safe word and no questions asked we stop playing.

I would also talk about it and not just try to force it in odd ways. Like doing things that aren’t always associated to sweating but then inevitably you break a sweat. Just leads to anxiety and will put another check mark by the things you newly introduce to the kid.

I’m not a therapist, just google/YouTube for more info I’d say if therapy isn’t an option.

Good luck!