Short answer: No, this "fix" is actually only required with !skins, you are correct in not being able to replicate it because your mods do not have this error. I only tested that it originally didn't work with !skins, this fixed the !skins error I was having, and so I just also tested your mod to make sure that this fix "also worked there" but I didn't actually test to see if the bug existed when only using your mod, only that it still all works together when they are combined. Entirely my bad.
Long answer: Sorry for the confusion! Maybe I should have been more clear or done more testing before writing my description, because obviously I just threw the extra work over to you, but I never actually tested if the error occurred without !skins. I also only recently found out that this bug is entirely !skins fault, and made the note on one of that mods discussions
Now this part might be beside the point, but just to also add on to how this current version is actually different from the other mods current version, I've got some issues opened with !skins (only like 2 days old because I reported late, that's my fault, absolutely no blame to Penguin_spy there) and actually have mods uploaded solely to allow compatibility with !skins and other certain mods, but this CharacterModHelper version completely bypasses that.
So just around 2 days ago was when I realized this issue, but I didn't realize how poorly my description was written to accidentally indicate that there is an issue with your mod, so my deepest apologies for making you do something for actually no reason...
"What is it? - Nuclear Science Crafting Fix is a small mod that fixes a compatibility error between Nuclear Science and skin swappers like !skins (Skins Factored), CharacterModHelper, MiniMAXIMe." - Is not true at all, it only applies to !skins, and I'll update it now. I realized something was off about my mods when I made that post, but I just wasn't sure what it was, again, sorry for making you do the unnecessary work, your mods have always been fine for me lol. It was just the fact that I use them all together that I wanted to "make sure they worked and were compatible" but I realize testing that the "fix" worked without testing if any of those mods actually broke anything was actually an incredible waste of time for multiple people that's kind of impressive, but I need to end this comment so there it is. Again, apologies for the confusion, and thank you because your mods have always been fantastic!