And quite possibly against the wishes of politicians and soldiers on both sides of the border. But probably correspondingly with the blessings of other politicians and soldiers from both sides, allies he had gathered during his years of "cowboy diplomacy" straddling that border.
I don't think the risks would have been too big. If Spock got captured, he and his captors and their loot would all be lost to the supernova anyway... A sidestep in spacetime notwithstanding. But the Vulcan Science Academy doesn't believe in those, right?
Even Countdown, with its weird ideas, seems to agree that all Vulcans believed Spock was right about the supernova threat - they just disagreed on whether Vulcan ought to help, or on whether Vulcan would be able to help. Sending Spock would thus guarantee either success or then the eradication of all compromising material and personnel. Win-win all the way.
Timo Saloniemi