When the weather is warm, is it pretty critical to skin the beaver the night ya get it, or can it sit in a shaded garage for a day or so without sustaining pelt damage?

Beaver keep better than probably any other animal.
Depending how long they have been in warm water dead in a trap, I would let the fur dry before skinning them(a day or so).If you are doing a two or 3 day check in warmer weather and the water is warm,you will have to skin them wet.

Let them dry then skin. Then once the hide Is off the carcass you probably have another day or two before you need to board It.

I let my 15 rats lay out on the tail gate In the sun for about 4 hours every one of them started to turn a bit green. But It's no big problem.

My partner, dying Beaver before we start skun'n...

I like to leave them lay for about 2 days . Skinning fresh caught beaver Is a bloody mess.

Im jealous of the time you northerners can let em lay b4 skinning.

Good info

and Hern, that's a cool picture with the leaf blower.