ok easy name a single time/moment, Laws used amputee not inside room.... Unless you have proof amputee even works outside of room.
Uhm, no, of course Law can use amputee only within his room. But that's the point, he was inside of his room. It's just that Law doesn't need to announce his room every time; it is self explanatory.
Reread chapter 690 of Law vs. Vergo. After Vergo finished fighting Smoker, he faced Law again who retrieved his heart. Upon Vergo attacking, Law cut him along with the entire mountain range. Yet we haven't seen him activating his room during all that time. He only activated a small room in 683 before being terribly beaten up by Vergo, ending up lying on the floor.
So Law, when cutting Misery, either activated his room, or maintained it all the time in the first place.
Law cutting Misery with Amputee is thus a far more logical explanation than randomly assigning to Law swordskill that goes even beyond the already advanced skill of cutting fire. Why aren't you just intellectually honest?