Well, that settles that…From a reader:

I’m not Stuttaford, but I’ll give it a try. No, I don’t think the
corbomite maneuver would have worked on Klingons, at least not good
Klingons, because dying while destroying one’s enemies would guarantee
them a place in Sto-Vo-Kor (sound familiar?).
They’d also have a better chance of knowing there was no such thing as
corbomite, since they have had spies in human ranks before (see Trouble
with Tribbles).