I’m not sure what kind of plastic paint thinner won’t melt, but I wouldn’t use paint thinner, especially on plastic. Unless you can figure out if paint thinner will be safe on the type of plastic the FHZ is made out of, I wouldn’t do it.
It really depends on what it was painted with. Did you do it or someone else? Quite a few people paint w/water based acrylics, in which case soaking in soap and water should work. You can remove the logo from the caps w/brake fluid and a q-tip. Other than that if it’s an enamel or lacquer paint, best to leave it be. Most anything that removes those will affect the plastic.