The reason I say to shoot quickly is not so much that you have a short self defense barrel, but I assume it has a fixed open choke. That means that your shot pattern will open up so quickly that the pattern is blown; the shot is spread so much that the target can pass through a whole in the shot column. With an open cylinder, I think it will be hard to break anything further than 25 yards out.
That is lilkely why oneounceload asks exactly what you intend to shoot. In formal trap, the targets are going away from you as they come flying out of a machine, kept in an a house, that is already 16 yards out. Hence you have to shoot it really quick with an open cyllinder choke. A common choke used for 16 yard trap is a modified choke.
In regulation skeet many of the targets are shot when they are much closer. some are going away from you, some come at you, and some pass in front of you. That is why many use a "skeet" choke. Skeet targets are often so close when broken that the shooter is showered with target fragments. I believe some shoot targets going away with a slighly tighter choke thqan a skeet but I am not that sophisticated. A skeet choke isn't much tighter than an open cyllinder and if you intend to set your back yard machine up to somewhat emulate a skeet machine my guess is that you may find it easier to break clay with your gun.
Whatever you do just be sure to set things up to be safe.
Experienced shooters please feel free to correct me as needed.