I suggest a compromise. Rather than shave with a razor and deal with the cycle of slick and velcro whilst wearing a beanie, touque or whathaveyou, get a beard and moustache trimmer and use that with no guard to clip your hair. It'll still look to the lay person like you shave your head, but the 1/16" hair won't grab your knit clothes the same way. Then when the weather gets warmer and the caps go away, shave it clean. Good luck!