I too have a 90% white overo with pink skin sheath, nose, and blue eyes (all pink skin there too). OP, you are miles ahead of many owners by providing sunscreen and finding a barn owner willing to apply it. I don't see the big deal in putting it on the outside of his sheath unless he is hard to work with & she doesn't want to get kicked. I have never had a horse get a sunburned sheath though, so I don't know how necessary it is for sunscreen to go there.
Skin cancer doesn't come from those small exposed areas, it just visually manifests around the genitals, anus, eyes and nose while the cancer can be everywhere. Your best option is to make sure he has as much sun protection as possible. Get a flymask, sheet, neck rug and possibly the leg boots with at least 75% UV protection as well as continue with the sunscreen, and your horse should be relatively safe. I also watch the UV index and if it is too high, my horses will have to stay in until it goes down, it is generally the highest between 10am and 2pm. I'm not a fan of night turnout because of the mosquitos, bugs and other animals, but thT is mostly because of where we live.
If it makes you feel better, I would be upset too if I were paying extra for sunscreen service & the BO refused to do all of what I was paying for. Whether it's needed or not, sunscreening a sheath would take me 2 seconds as oppose to the 2 minutes it takes to do a nose so the horse can't wile it all off. The best thng to do is to talk it out as politely as possible.