We have been painting 2% Lugols for 1 1/2 years and we've not had it stain the skin. Trust me, I would not tool around with an orange glow on my face if it did that. It does not. Especially when I paint it on first, then massage in things like jojoba oil and the like.
Wombat's Iodine salve tho is just the ticket. It is wonderful for doing so many things topically, and no, it does not stain. Least not here.
Now watch, you'll try it out and end up looking like the great pumpkin monster and then yell at me. Trust me tho... 2% or weaker, or Wombats salve... no staining. Honest. Nothing a little ivory soap and warm water won't wash off. I believe I am fairly well saturated with Iodine and note that painting does cause Iodine to linger on the skin much longer. But soap and warm water, and things are right as rain.