For the shotgunning games you listed I believe that you will find that a longer barrel will be a definite plus.
Consider these facts: The top shooters in Skeet typically use guns with 28-inch (minimum) barrels; Trap's top shooters typically use guns with 32-inch barrels in over/unders, and that length or longer in single-barrel guns. Why? Because as the late Gene Hill put it, "A gun that's too easy to start is also too easy to stop." In other words, guns with shorter barrels may feel "quicker" to get on the target, but their lightness can also encourage the bad habit of checking (stopping) your swing instead of following through, resulting in misses. The momentum generated by the longer, heavier barrel helps smooth out your swing, promoting proper follow-through and more hits.
Before you make your purchase, try shooting a few rounds of Skeet or Trap at your local gun club using a gun with a 28-inch barrel v. a gun with a 30-inch-or-longer barrel (making certain that the guns properly fit you) and see with which you perform best.
Good luck, and good shooting!