let out a little faux knee-slap

<I've been sleeping like a baby,'' McCain told The Tonight Show's Jay Leno last night - "Sleep two hours, wake up and cry, sleep two hours, wake up and cry.''
McCain let out a little faux knee-slap for his well-timed, if well-worn, joke.>

“A knee-slap” is a very funny joke.
I don’t understand the meaning of the last sentence – McCain let out …
Please help.

Thanks.

A "knee-slapper" is a funny joke. A "knee-slap" is, well, a knee-slap. Anyway, back on point. "Let out" is usually used to reference a sudden involuntary vocal exclamation such as a shriek, laugh, gasp, etc., so their usage is baffling to me.

Example: "While watching a scary movie Robert let out a loud shriek, much to his embarrassment."

What they should have written:

"I've been sleeping like a baby,'' McCain told The Tonight Show's Jay Leno last night, giving a faux knee-slap for his well-timed, if well-worn, punchline. "Sleep two hours, wake up and cry, sleep two hours, wake up and cry.''

Still in the dark: “faux” along with ‘well-timed” and ‘well-worn”; let out a knee-slap for a joke. ???
Please elaborate.

Some people slap and punch things when they laugh for some reason. So Mr McCain started laughing and slapped himself on the knee. 'Faux' means it was not genuine. A 'well-timed' joke is one which is made at the best possible moment with the best possible impact. 'Well-worn' means it is a cliché that has been used by many people before - not original.

Aha. Well-worn is hackneyed / trite. Yes, used by Bob Dole in 92, Kathy Karpan in 96 and Bush in 2000.

Some more questions.
Why “if’? if = even though?
“a little knee-slap” or a knee-slap which is “a little faux” ?
Why faux and not false?

It seems to me he neither laughed nor made any gestures while saying that. Could I have missed?