Hello, sorry for the slow response!
it's not possible to export parts individually, but it's possible to export to an atlas that you can then crop by yourself, as seen here: https://mochakingup.itch.io/cc2d/devlog/160176/update-v170-and-undead-pack
but as another user just pointed out in the forum, this is currently bugged in version 1.90, so please stand by for a fix on that.