Hmmmm........let me offer some thoughts.
The answer to your question is NO to the best of my knowledge. What most people don't realize is that humans are rarely allergic to cavies. It is most often the type of hay that is being used. Timothy hay is the worst allergen. When we first started keeping cavies this go-around, my husband had a major allergic response that ultimately led to repainting the room, professionally clean the sofa, and move the boys into my small home office. He went to the doctor for testing and sure enough it wasn't the piggies.
We spent the next month searching for a substitute for timothy, fed the boys no hay except for hay cubes, and thoroughly cleaning everything. We finally landed on bluegrass hay and later orchard grass, both of which provoked no allergic response. Of course, if you choose to eliminate the present hay, then you must thoroughly clean everything in the cage AND bathe the piggies because they have the hay spores in their fur.
Now having said all this, you seem to have thought through this current scenario. If absolutely everything is the same as your girls' setup, then I would first thoroughly clean the cage that he is in AND consider bathing the boy to possibly remove any traces of anything he could have in his fur. Perhaps someone who has more expertise than I will come along and offer suggestions, namely our esteemed moderator @bpatters.