It's actually from the hair type. I can hold my heeler mix who has soft Am. Eskimo fur and don't get the bumps. If I hold the Basenji's or the Boxer I get them. It's from the short, prickly fur. Since Shadow now has a Neuter coat I don't get it as bad from him.
I am new to this site but I can say that I have had dogs all my life and I now have four Basenji's and I only have one of them that gives me those bumps. My doctor says it is the hair texture and environment. The hair is so short on her that I pick up all the allergens that she is holding on her skin, All I do is wash her off with a wet towel before I touch her and we are great. Maybe you could try that..