Beware of hubris. That's the only reason why this would be rude or insulting.
I will tell you how I would handle such a situation, for an increased friendliness with the other player. It's almost totally disrelated from the actual strategies of chess; this has to do with interpersonal relationships.
As a fairly decent chess player, I still have a great deal of humility. First of all, if I am only fairly certain I have checkmate in three moves, I would not want to assume that there is zero possibility that I have overlooked something.
In the case where I have double and triple checked the finite possibilities carefully and know that there is zero chance I've overlooked something—I know it is mate in three—there is also zero harm (and much benefit!) in communicating it as a belief rather than a undeniable certainty, at least at first.
What I would say if I determined I had a guaranteed mate in three is:
"And, I believe that's mate in three. Do you see any way out?"
People are much more willing to accept things as true that they see for themselves. Of course they shouldn't just believe you. They should see it for themselves. And presenting it in this particular way opens the possibility for a dialogue, which is much more friendly than an adversarial relationship.
In this way you could guide them—without any arrogance or hubris—to be able to see the "mate in three" that you have your eye on.
They will either discuss the possibilities with you ("No, it isn't mate; what if I move my bishop?" "You would think—but don't forget about my rook!") and then finally conclude that it is checkmate—or, if you have overlooked something, maybe they will see it and the game will continue! And you will have learned something.
Either way is fun. Why be serious about it?
On the other hand, if your goal is just to prove to other people how much smarter you are than them, then the above method won't work at all. But in that case you have other problems than winning a chess game, like how to make friends. ;)