Yay! Electronics and costumes, two of my favorite things...
Normally I'd be the last person to discourage anyone from trying techy stuff like this...but wings in particular...I've seen some really
gifted engineers and costumers just totally defeated by this exact problem, repeatedly. It can
be done, but it's a pretty advanced Skill Level 5+ type of project requiring a lot of trial and error (mostly error).
As an alternative, I've seen a number of manually-controlled wing sets that are discreetly operated using well-placed cords and hand loops (and practice). Look around on YouTube for 'articulating wings' for some good examples. Sometimes low tech is best.
For the projection aspect, that sounds much more approachable for a first-time Arduino project. But I'd need to know a bit more what you had in mind.