I own two pairs of polyester/lycra boxer briefs that are what I use on hikes. They fit like a glove and prevent this sort of irritation by being very slick.

The lightest solution is pantyhose. Cut off the legs if you feel your manhood is threatened, but the nylon will minimize friction without impeding sweating. Does the same thing as biker shorts for 1/4 of the weight. I also hear a girdle without the stays will also do the job, but I've never tried that. The guy that told me about it used to get blisters on his hips from the hip belt as well as the inner-thigh irritation, so it solved both problems for him.

You're getting the rash because your clothes are rubbing against some relatively delicate skin. You want a form-fitting garment to minimize that.