If you cannot find any cycling arms without silicone grippers, how about adapting a fashion item? Take white long-sleeved item from charity shop, Primark, back of your wardrobe. Cut all round the body just below the shoulders. You now have a pair of sleeves connected by a collar. No grippers present or needed. Simply pop it over your head for sun protection. You might want to hem the new, erm, hem, if it's intended to last more than one or two adventures.
Alas, I can't think of a way to do this for legs.