"Live"traps :-
The term live trap is used to describe traps which catch and hold the intended quarry rather than killing it. Several forms of live trap are used the Larsen trap is just one of them. They are usually constructed of very strong wire or "weldmesh" as they have to withstand the struggling of the caged animal or bird until the keeper arrives to dispatch it. The keeper will visit the traps every 24 hours minimum as legally required and dispose of the animal or bird humanely, re bait and then reset his trap so it can continue it's work. The live trap is an excellent method for catching rabbits but may well be used for rats, mink, stoats, weasels and even foxes in some cases.
Air rifles :-
Air rifles may be used in "ambush" for winged vermin and ground vermin but obviously they are only active as long as you're there. A good air rifle can provide a certain amount of protection from crows, magpies etc but please remember to use a gun suitable for the task, an airgun is not suitable for shooting foxes. Unless you hold a firearms certificated airgun the legal limit is 12 ft/lbs for any air rifle and a good degree of accuracy is a pre requisite as with any live quarry shooting. Air rifles can provide a few hours of sport and much needed protection at times when and if the quarry becomes wary of cage traps.