Is it possible to change the order of perks for the Specialist strike package?

The order of the perks granted by Specialist is the order they are selected in. For example, I can set it up so that Assassin is my first extra perk, Extreme Conditioning is my second, and Stalker is my third.

The only restrictions placed on what perks may be selected are the three perks you already have selected outside of Specialist, and perks that you have not yet unlocked.

Just deselect all of them, and then select them in the order you wish for them to be applied when getting kill streaks.