I have a friend with the same issue. He wore short sleeve shirts all year round to avoid the problem of getting the shirt cuffs wet. When he came down with pneumonia, I insisted he buy some long sleeve shirts to keep warm. He raised the issue of wet shirt cuffs with me. I told him it was not a big deal. Wet shirt cuffs will dry. There is no need to wash all the way to one's wrists. I usually stop just above the knuckles and do the thumbs separately. I think Purell is a good product but it contains alcohol which is drying, especially in winter weather.