It's also clear that Kirk knew he was being had. His inflections when he says "I hope we won't have similar opportunities to test those orders which you, umm, never heard" are rather obvious...
Timo Saloniemi
And the shooting script has a bit of helpful information.
The final draft script for "The Tholian Web," dated July 30, 1968, has the following dialog and script direction at Scene 138:
KIRK
(blandly contented....)
I hope my last orders were helpful
in solving the problems not worth
reporting.
Spock and McCoy look at each other questioningly and then
look blankly back at the Captain.
SPOCK
Orders, Captain?
McCOY
What orders are you referring to, Jim?
KIRK
(a knowing glint in his eye)
The orders I left for you...for
both of you...The taped orders I left.
MCOY
Oh, those orders! There wasn't
time, Captain. We never got a
chance to listen to them.
SPOCK
The crisis was upon us and then
passed so quickly. Captain, that...
KIRK
(smiles)
Good! Let's hope there will be
no similar opportunities to test
those orders you never heard.
(looking at viewer)
Warp factor two, Mister Sulu.
SULU
Warp factor two, sir.
So, the one script direction that provides any information on the writers' intent on how the scene was to be played by the actor is the "a knowing glint in his eye" direction. It looks as if Kirk was supposed to have suspected Spock's and McCoy's little ruse.