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Like others said, cut the liners out out of your shorts. Buy a few different brands of boxers or briefs that don’t absorb sweat much and see what works.
I went through 5 or 6 different models of lined shorts before I realized I just needed to find good sport boxers where everything sits right and cut the liner out of running shorts.
Penatin cream.
Mens Rabbit brand split shorts or just mens Rabbit brand regular running shorts are good since they’ll give you a lot of non coverage on sweaty balls except then you’re basically free balling.
Their shorts seem to be made for MTF male to female trans individuals I am guessing as the balls of a male will usually hang outside of the shorts liner based on the way the shorts are cut. Not a huge deal unless you’re sitting on a track doing some hamstring or groin stretching