From my experience, the old guy that gave me some pointers when I stated trapping told me, "Those fleas are not going to bother you the first year, but you will get bit and scratching the second year". I do not know the reason, unless it was catching so much fur, but these were red fox, and he was dead on about the fleas. The second year I had bites and red marks all over.
How I handled it was to get a garbage bag or bit plastic container, put the animals in it, and sprayed it with Raid, Yard Guard. Rubber gloves help too, and I never used it, but probably Deet on the sleeves of a skinning jacket to repel them.
I have never had any problems with other species, and the only people I ever knew who had flea problems was my Aunt who had a miniature poodle, that either died or they took care of the fleas, and those things came out of the carpet and gnawed on the people afterwards.
I would think having some common sense and using capped large containers in a van with insecticide in them that would not kill you, would handle the fleas. Is a point though on too much fly spray in my brother used to pick up milk from dairies, that had those fly misters always spritzing in the milk room, and he got dizzy as a bat from over exposure.
Is the point, in I have a pick up, use a weight in a plastic container and spray the fleas dead. Is harder pealing, but day old critters usually do not have fleas and if they do they are slow from the cold. Problem seems to be too many people with luxury items like heat and a building to skin in. (last part is satire)