Re: Pump shotgun for skeet and trap
Back when I was in junior high and high school, I used an 870 to shoot trap in the local league but had a chance to try out a few of the other guys' guns too. Still use one whenever we get together to informally bust a few pigeons. I never had a problem with follow up shots or doubles. Being a small town and farming area, it was pretty much run-what-ya-brung. There weren't a lot of guys shooting high-dollar guns, most of us shot field grade guns but some had specialized trap guns too. There were a few guys shooting Red Label, Superposed, 3200, and a couple of Weatherby O/Us but most of the folks used a pump or semi.
My experience is that once you get the action down you'll have a pump action cycled before you recover from the recoil or swing to the second bird anyway.
Never shot formal skeet so I couldn't say about that game.