I havent personally tried it but I think that some frozen wrist bands or a vest with insert spots for ice packs, would each be more effective and convenient.

Something like this:

https://www.amazon.com/Cooling-Fishing-Cycling-Gardening-Motorcycle/dp/B07VCSQ1WM

Or this:

https://www.amazon.com/Cool-Wrist-Ankle-Chemical-Medium/dp/B074VGHYF8