It's actually really super simple, and on an Up Up & Away (who is already pink) you will have no problems with staining at all.
All I do is put a tiny bit of Rit dye in boiling water, dip the pony's mane and tail in for a sec, then rinse thouroughly with cold water. If it's not quite dark enough, repeat. Usually it only takes one swift dip and they're restored to their original pink shade, but I've had a few stubborn ponies who take three quick dips to get the original shade back.
I've never had it stain a pony because it's simply not touching the plastic for long enough! Move fast, but not sloppily, and be sure you don't spill dye on anything else that will stain (like laminate kitchen counters!)