Paint removal

Will paint thinner melt FHZ plastic

Yes

Do you know anything that will remove the paint without harming the plastic

It depends…

Lacquer thinner will melt it, mineral spirits will not.
What to use depends on the type of paint. Ordinary acrylics will probably come off with soaking in water. Enamel may come off with mineral spirits. Maybe use some steel wool to rub it off, use it wet.