I’m not sure if the weight would be enough to trip the lever, haven’t actually used one yet, but you could try a cat trap?

I’m just concerned for a domestic bunny is all. Other than cats there’s wet grass and disease

Edit: Never mind, apparently they don’t work well for bunnies. Some better advice here https://www.ohiohouserabbitrescue.org/i-want-to-learn/tips-for-catching-a-stray/