The whole thing has been painted? I reckon it's a lost cause mate. You could probably remove a few drips and still preserve the finish, but if the things have been coated in paint I think your best bet is to take the lot off and re-wrap.
I reckon you could do it, but you're in for a bit of work. I just took the wraps off of my drums and had a great time with some really fun chemicals like acetone and mineral turpentine. Couldn't see straight for about a week, but in the end they look great.
You might procure yourself some o that stuff and try a spot test on the paint. Can't hurt, cause as PFOG said you might need take the wraps off anyway, so you'll have the gear.
Most drum restoration guys use a citrus based paint remover and a PLASTIC scraper if need be.
I have used a product called Mostenbockers graffiti remover on 60's vintage wrap,and the stuff is just amazing.It dosen't harm the finish at all.
Even if your wrap was in need of cleaning or polishing,you can use a product called Novus.It's a great plastic polish and scratch remover and comes in 3 different grades.Use the least abrasive one first ,and then see what happens.
I've done a restoration on a late 40's Radio King snare that was painted,and it came out great.
Another recommendation for citrus based removers. I've used it to successfully remove stencils from road cases. If may soften the plastic a bit but it has a chance at recovery. My road cases were a touch sticky for a few days but hardened back up.
You could also try rubbing compound if the paint was sprayed on and not too thick. This will take some care not to cut into the wrap too deeply and pit around the sparkles.
Jasco is methylene chloride which will attack any plastic like the sparkle wrap and really eat it up.