If you don't like the idea of traps, how about using a ferret instead?
This is the first time I've tried ferreting. The concept is simple: Find a rabbit burrow with multiple holes. Using little purse nets, cover every hole you can find. Pop the ferret under a net into the burrow and let her (females are best) hunt the rabbits. The rabbits run in fear, bolt out of a hole covered with a net, and get caught. Rabbits can be dispatched quickly (and turned into rabbit curry later).
I shadowed Winsor, a keen ferreter. He was hired to clear out some rabbit burrows undermining the formal lawns at the big house. Moles and rabbits create soil mounds and hollows when burrowing. Mounds and hollows are tolerated around the informal parts of the garden, parts that are mowed with a giant tractor or grazed by sheep. But, in the formal gardens, the soil mounds ruin the blades on fine cylinder mowers, upset the flat surface of a croquet lawn, and are generally unsightly.
Ferrets are of the mustelid family. Most mustelids in Britain are the bane of a keeper’s life: mink, weasels, stoats, polecats, even badgers. Ferrets are unique as most can be tamed by feeding and handling (there’s always some that hold on to their independence and bite when handled.)
Unlike working dogs, ferrets aren’t trained. Ferrets simply follow their instincts to hunt, and rabbits follow theirs to run away. The ferreter's job is to set the nets and redirect the ferret when it emerges from a hole by popping it down the next nearest hole.
I spent most of my time in this position -
Face down under a bush setting nets. Or popping ferrets back into holes. There's not a lot of training required for the humans either. The ferret does all the work; the ferreter just adopts the laying down position. As far as vermin control goes, this is pretty low cardio.
We worked along the walled vegetable garden. There were so many rabbit burrows underneath the wall that I was surprised it hadn't fallen into a giant sinkhole long ago.
The ferreter and I worked the outside of the wall, and underkeeper Ian waited inside the wall. We set nets on both sides to block both ends of a tunnel. It's easy to hear when the ferret is on her prey: the rabbits make a rumbling noise stamping their feet and fleeing. Then, WHAM! out of the corner of your eye you catch sight of a rabbit bouncing about, the drawstring purse net pulled taut around it. The ferreter’s only other job is to despatch and gut the rabbit (and, in my case, make the curry later.)
When it works, it's magic. But the odds are in the rabbits' favour. No matter how many bushes you crawl under, there is always one hole left uncovered. Inevitably that’s the hole a fleeing rabbit will choose for its escape. No net = no rabbit = no rabbit curry for dinner. We caught 3 rabbits this time. We lost 5 more to an overlooked hole.
Ferreting works best in winter, and by spring/summer we are back to shooting the odd rabbit when we see it. And rabbit salads instead of curry.