The way I always read that scene is Frasier knew it was the echo button but wanted Clint to look foolish when he used it as a cough button.

Actually, I don't think so.

That would be malicious, and Frasier is often enough a pompous ass with aspirations to become a *real snob*, but he is not malicious.

He always falls flat on his face when he tries to be clever, or sneaky; that never ends well. And although he can be a bit of an ass, most of his bad faux pas are genuinely unintended.

Frasier is one of the few sitcoms that are still palatable *because* there is so little of the viciousness of most other sitcoms that derived their 'funny' moments from being vicious, unfiltered outspoken, and hurtful.