What the heck, I'll dig in. Even though I know I'm way over my head.
I've never read
The Prince. But regarding the question in general... who's "relabelling" anything? I only ask because I get the impression from your post that the individual is taking it upon themselves to relabel good as evil or evil as good. I would say God is the one who decides what is what. "Good", "evil", "righteousness", "sin", etc. are all ways of describing conformity or non-conformity to God's will. God's will determines totally what is objectively sinful and what is not. Acts are sinful when they violate God's intended purpose for the way things are supposed to be. (A purpose which we can never know 100% for certain in individual situations. Therefore, we must try to apply the broad principles we learn in his Word in our life circumstances as best we can.)
Maybe an example could be, "Thou shalt not kill" is a commandment, and yet David was considered a great king for slaying many of the enemies of Israel. (Under orders from God.) David's bravery and strength in battle could be a virtue, perhaps. Yet, if he lost control and became an indiscriminate bloodthirsty murderer, killing would become a vice. The difference is the former killing was commanded by God and was in line with his will; the latter was not.
Or, "Thou shalt not bear false witness" is a commandment, yet Rahab the prostitute was considered God's friend for lying about the Hebrew spies hiding in her home. Her courage to protect them could be considered a virtue; yet if she became a compulsive liar and began to lie to suit her own ends it would become vice/sin. The difference is one use of lying is aiding God's plans and one is not.
The "characteristic of sin" never changes in that sin is always that which is in violation of God's will; the Greek word for "sin" in the New Testament,
hamartia, literally means "to miss the mark", i.e. the mark of God's perfection. But that means we need to know what God's will is in the situation at hand in order to avoid sin. How do we know what God's will is? We read his Word, we pray, and we do the best we can to try to figure it out. And if we fail, we'll be forgiven.
Does this make sense?