Bacon Bits
Legend
A default assumption on the use of Nick is that it has to be on the weapon that you make the extra attack with. That is, if you attacked with a shortsword + scimitar, the scimitar would be the offhand weapon because that's what you're making the extra attack with, and thus would have to be the weapon with the Nick property in order to gain its benefit.
I don't think that assumption is actually supported by the text of Nick. I think it's left intentionally ambiguous. Every other mastery property explicitly states "this weapon". Nick does not. Indeed, it just backreferences the Light property.
It would have been really easy for Nick to read: "When you make the extra attack of the Light property with this weapon, you can make it as part of the Attack action instead of as a Bonus Action," or they could have said, "When you make the extra attack of the Light property and you have already attacked with this weapon, you can make [the extra attack of the Light property] as part of the Attack action instead of as a Bonus Action."
But they didn't do either of those things.
I think it's as wide open as "If you're using two Light weapons, and one of them has Nick, and you have mastery of that weapon, you can make the Light attack as a part of the Attack action intead of as a bonus action." I really think the rules just don't care if you attack with scimitar or shortsword first.