Oh... LAUNCH doors... I read that wrong, so it does mean you can still run...
Given the status as a simple "henchman", the best bet would be to run. lassev summed it up quite nicely; henchmen don't kill the hero, and stopping them would be futile. BTW, just for ideas, where would this silo be located? Siberia? Kazakhstan/elsewhere in the southeaster former USSR?
BTW, There would be a simple way to prevent the annihilation of the silo, given the right tools (very possible, given that we'd be henchmen actually getting close to the hero), and enough time (mabye a minute or so, or any ammount of time that would be enough to escape from an upcoming thermonuclear blast). Just take whatever you have, and start trying to destroy the missile. If you're lucky enough to avoid detonating the conventional explosives in the device (a 0% chance while the hero is still in the silo anyway), you can remove key parts of the trigger, and preven the missile from detonating. However, if there's no system for the exhaust to escape, you'll just be incinerated with everything else in the silo. It would be better to disable the engine system, so it wouldn't launch in the first place.
...See, I wouldn't fit the role of henchman very well... I see myself more as the mad scientist or mastermind... I have the evil laugh to go with it as well. ::lets out his evil laugh::
Wake up, George Lucas... The Matrix has you...