There's nothing impolite about delivering checkmate in the same fashion that you'd make any other move. If anything, e.g. in formal games and when there's no risk of losing on time, it might be considered bad etiquette by the losing player to continue playing on in a completely hopeless position, instead, players usually resign before the checkmate occurs (see also here for related discussions on etiquettes fo resigning or playing on).
As to what the right etiquette for giving checkmate is, there isn't really much to it and you've basically already summed it up, that is (in the following order, with first two points being most important assuming a formal game):
- Typically, one simply delivers the checkmating move,
- presses the clock (a move counts as officially registered [*] once the clock is pressed while your flag hasn't dropped).
- and wait for your opponent to realise the checkmate if they haven't yet (also typically further signalled by making eye contact),
- at which point they will extend their hand for the final handshake of the game and scoresheets are signed.
On a more fun note, sometimes resigning before checkmate can become a bit awkward too when the losing player realises checkmate is imminent having missed a combination, like in this game between Nepomniachtchi and Sarin, and sometimes delivering it can be plainly awesome like Ivanchuk checkmating the world champion ;)
[*]: This is to be on the safe side (in case the move wasn't actually checkmating), even though as pointed out by JiK in comments, according to FIDE rules (220.127.116.11) if a move ends the game, it is completed by default, i.e., pressing the clock is no longer necessary when it is either a checkmate or stalemate.