In situations where I need to handle squirrels and might get bitten, I have a pair of thick wool mittens with a leather mitten shelf outside them. Even if an adult squirrel chomps down and their teeth make it through the leather and wool, the teeth do not reach my hand.
I have used these mittens many times, mostly when taking care of injured squirrels.
I had one squirrel (Harry) about 3 years ago that was being overwintered who got extremely aggressive at about 6 months to where beyond the usual double layers of clothing and the wool/leather mittens I actually had to wear a fencing mask to protect my face.
Yep, he actually bit me right in the cheek. I was using one of those big plastic face shields like for using a weed whacker and he got up under it and gave me quite the bite.
After that, I went with the fencing mask, tucked under my hoodie with a towel tucked in over my throat.
https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1