Will auto shop employees question my manhood if I ask for wiper installation?

They will not laugh at you, a lot of men have know idea how to put on wiper blades its no reason to ashamed. A lot of guys will have them installed for them so they don't have to get dirty. They should be professional with everyone man of woman, young or old. That is why they get paid by the hour from there employer. Most places have installed a lot of wiper blades and they will be able to do it right and fast for you.