A Swift Action Can Be Taken During the Surprise Round
The Surprise Round says...
If some but not all of the combatants are aware of their opponents, a surprise round happens before regular rounds begin. In initiative order (highest to lowest), combatants who started the battle aware of their opponents each take a standard or move action during the surprise round. You can also take free actions during the surprise round. If no one or everyone is surprised, no surprise round occurs.
Emphasis mine. Then there's this about Swift Actions...
A swift action consumes a very small amount of time, but represents a larger expenditure of effort than a free action. You can perform one swift action per turn without affecting your ability to perform other actions. In that regard, a swift action is like a free action. You can, however, perform only one single swift action per turn, regardless of what other actions you take. You can take a swift action anytime you would normally be allowed to take a free action. Swift actions usually involve spellcasting, activating a feat, or the activation of magic items.
Emphasis mine. So, yeah, swift actions are allowed in the surprise round.
Unlike other games in which characters can take more significant actions to perform less significant actions, Pathfinder and its antecedents have firm limits on the actions that can be taken during a round, including the surprise round. Actions in Combat says
In a normal round, you can perform a standard action and a move action, or you can perform a full-round action. You can also perform one swift action and one or more free actions. You can always take a move action in place of a standard action.
In some situations (such as in a surprise round), you may be limited to taking only a single move action or standard action.
Other than taking a move action instead of a standard action, there's no way under normal circumstances to take an action of one type in place of an action of another type.
- During his turn in the surprise round, a character can't take two swift actions, replacing the move action or standard action he's normally allowed with a second swift action.
- During his turn in a normal round, a character can't take three swift actions, replacing the move action and move action or standard action he's normally allowed with a second and third swift action.