I usually but the ultra thins without wings as AF is so light. But on the occasions that I do use ones with wings I wear an extra pair of undies over the top - keeps the wings from unsticking and keeps them hidden.
I've very rarely had a wingless one move.
Don't even get me started on the packaging though! Why the ridiculously bright packs??! I'd prefer to be discreet thanks, rather than having some fluro bright pack in my trolley attracting attention and announcing to everyone in the supermarket "I'm on period!! Just in case you were wondering..." ugh! Seriously 😬