It’s up to you if you let yourself craft them early, though they generally will just appear as regular variants of the non-unique versions.
I did my best to make it so that you can’t obtain these mods unless you complete the quest for them, but some of them don’t have quests attached (as far as I could see, correct me if I’m wrong), so I wasn’t able to do that for all of them, unfortunately. And before I go any further, this will be pretty spoiler-y if you don’t want to know about any unique weapons, so don’t go any further if you don’t want to be spoiled. This has been part of Cut Weapon Mods Restored for a while, but I decided that it doedsn’t really fit as a set of “cut” mods, and that it was more deserving of a page to itself.