The vet's office might be concerned about the fleas spreading to other animals. In addition, they may be concerned about the possibility of the fleas spreading disease.
You should call the vet's office and ask before bringing him there.
This is a guess, but it might be a good idea if you were to completely wrap the body in a good cotton cloth. You could also use a sturdy cardboard box, or a wooden box. This will be a barrier to the fleas, and will be destroyed in the cremation process.
I suggest cotton, cardboard, or wood because these are made of natural fibers, and will work well with cremation.
I'm sorry for you loss.