If the hook is in the outside jaw it is legal. The reason the rule says "mouth OR JAW" is to specifically address fish caught on the outside of the jaw. Read every word in the law as if it has meaning.........(i.e. why mention jaw if you mean mouth...?)
"(6) Fish not hooked in the mouth or jaw,
except those legally taken by snagging, snaring,
grabbing, gig, bow, crossbow or underwater
spearfishing must be returned to the
water unharmed immediately."
I don't know about IGFA, but this would be legal in MO under MDC rules.