If I had Animorph powers, I'd do one of two things:
1. If I was demorphing in public, I'd plan ahead and morph something with no clothes on (as someone else said) in privacy. Like, a dog or something you'd see on the street. Then I'd go out with a friend who's in-the-know. I'd have him overact and put on a big scene in front of people (maybe he'd wear a costume) of "casting a spell" on me. He would dramatically "change" me, and I'd overact too while demorphing, spazzing and twitching. Then, once demorphed, I would continue to act like a dog, walking on all fours.
2. If was was morphing in public, I'd do the reverse. I'd wear a lightweight T-shirt and some gym shorts, and have my friend do the same "cast a spell" thing, though this time I'd morph something "fantasy" like a frog or... a lizard I guess. Spazzing the whole time, and doth protesting.