
Talonhawke |

A command word can be a real word, but when this is the case, the holder of the item runs the risk of activating the item accidentally by speaking the word in normal conversation. More often, the command word is some seemingly nonsensical word, or a word or phrase from an ancient language no longer in common use. Activating a command word magic item is a standard action and does not provoke attacks of opportunity.
So no he can't fire it and say the command word in the same round.
Also a feather isn't fon go far out of a sling shot.

Norren |

A party member would need to utter the command word for him via readied action. Assuming he provided that, and that the shooter did something to get past the fact he's shooting a token (tying it to a rock maybe?)
There's a fall damage chart based on size under environmental rules, a swan boat holds up to 32 medium characters or 8 large characters, scaling up... that'd be 3 huge, I believe gargantuan is 4x4 so 2 gargantuan, or 1 colossal, so it'd be colossal?
Colossal on the falling damage table is 10d6. A note says "objects made of lighter materials might deal as little as half the listed damage, subject to GM discretion." and gives an example of a huge boulder vs a huge wagon, with the wagon doing half damage. It also says that if an object falls less than 30 feet, it deals half the listed damage.
It seems reasonable for a swan boat to be lighter than normal, so half colossal (5d6) and if they just shoot it straight from their normal sling range increment of 50 ft, that really wouldn't be falling... your choice of dealing either 2d6 or 3d6, or the "full" 5d6?
Cute, but somehow less impressive than what they were hoping for, I think.