Anybody made a shotgun slingshot?

I need to rid a wooded area of a rat infestation. The buggers are quick and used to my plinking at them with slingshots. They dart about in the undergrowth so fast I can hardly ever get a good shot at them. Firearms aren't allowed in this situation nor is poison or traps because of other wildlife complications in the area and it's a sort of public animal reserve with a lot of stuff living there, but it's overrun with rats that eat all the bird eggs and dig tunnels everywhere. Every time I go out there I try to shoot rats with my slingshots but they're canny buggers and hard to pin down.

I know the Right Honourable Reverend Jörg Sprave Of Infinite Wisdom made a cracking good shotgun slingshot but he did a lot of work making a shot holder for it (out of metal I think) and I'm not that talented.

When I was a kid I used to sometimes get up to stupidness and one of my little tricks was using BB's. Back then apart from the usual cardboard tube containers of BB's you also used to also be able to get these little individual cellophane packets of like a hundred or so BB's for almost nothing and they were fun to use with my Wrist Rocket.

I'd cut a little split in the packet with my pocket knife but not let the BB's spill out, and then shoot the packet over the rooftops of the nearby trailer park and listen to the rain of BB's clattering down on people's roofs, followed by a swift getaway on my bicycle.

I also remember having some of those weird .22LR shot things that were basically tiny little shotgun shells for a .22 and they were sort of fun but I can't use anything like that here.

I do a bit of slingshot creating and have a welder and a garage full of basic tools, nothing fancy, so I'd be interested in what you all think might make a shotgun slingshot.

I've also got a 50# pistol crossbow and an old speargun that I could sacrifice to the design maybe, but the whole thing needs to be discreet and portable on a motorcycle without looking like an extra from Mad Max, so it needs to be not much bigger than a slingshot really.