Decisive Strike does not work with secondary natural attacks.
Does it work with the Snap Kick feat?
The feat Snap Kick says that, in exchange for suffering a −2 penalty on all attacks this round, "[w]hen [the creature] make[s] a melee attack with one or more melee weapons [it] can make an additional [unarmed] attack at [its] highest attack bonus" (Tome of Battle 32).
Thus, despite the alternative class feature decisive strike (Player's Handbook II 51) mandating that its user realize its benefit by taking a new and unique kind of full-round action, during that full-round action, the creature using the feature decisive strike, in fact, does make an attack, and, because the creature is making an attack, the creature may also opt to enjoy the benefit of the feat Snap Kick.
Note, however, that using the decisive strike ability and the feat Snap Kick in combination sees a low-level monk suffer a total of a not insignificant −4 penalty on the decisive strike attack roll.