If he isn't prolapsed, it appears he could be headed that way. The soaks may float out any foreign material that could be irritating and inflaming his equipment.
Do you have any cortisone cream on hand? You can use that to help reduce any swelling.
A disclaimer: I am not a geese farmer. I am not a vet.
Make a tub of warm Epsom salt water and let him have a nice long soak, as long as he wishes.
For now, lubricate his "equipment" to keep it from drying out in between Epsom salt soaks, which he can have a couple times a day.
Call around to...