I'm trying to make a custom skin for some non-human Sims. I've gotten it to work on BodyShop just fine.

My question is, will this skin be enabled for new Sims? How do I make it so Sims can't randomly get this skin, just the ones I create using it? Thanks!

Skins directly from Bodyshop won't be enabled for townies, so that skin should already be fine if you don't want other sims to get it.

Directly from CAS the skins will be selected 50/50 at birth if the other parent sim has another regular custom skin (not towniefied/geneticized). The skins can also be inherited via the recessive trait from previous generations.

Custom skins are usually dominant over default skins, at least during the first/second generation, but after that it depends a bit on which skins the sim has in their genes (sims have one dominant and one recessive trait, and passes one on to their offspring - if both parents have a default or geneticized skin, sims get any skintone within their parents' range. If both parents have a custom, non-geneticized skin, the skin range is ignored and the offspring get one of their skins. If it's a mix, the custom skin tends to be dominant. Multiple generations can mix in some recessive traits, so it's possible to get previous custom skins or defaults popping back up after several generations)
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If you want skins to show up "semi-randomly" on ingame-born sims and townies, they have to be towniefied and/or geneticized.
Tutorial here: https://rikkulidea.livejournal.com/21779.html

That's a big relief, thank you!!