I am completely complacent with killing animals if need be. In our country a disease was released which blinds rabbits in order to kill them, I've forgotten the name. Once I stumbled across one and was only walking so I picked it up, put it on my lap and waited until it had calmed down, and had it in a petting like manor, then quickly broke its neck. All you can do is leave it to starve or kill it.
I don't get creeped out by killing but it all depends on the circumstances on which you should in good conscience decide to kill an animal.
The first thing I would have done if I found rabbits down at the end of my garden would be to see how it got in... and block the hole. This way, your stuff can go unmolested and the rabbit can live.
If you can't close the gap... why the hell not? If its all open then your asking for it to be had by animals

Now if they are literally breaking into your garden the all you can do is to kill the ones that enter your garden, although one should be enough to keep them away for two or three generations.
I haven't actually tried this but... maybe a warning shot? If you shoot above the rabbit, it may fear for its life so much that it won't come back! Which is a win too.
Killing, no matter what should be a resort only when everything else has been tried first. Does help to keep you guilt free in the situation you described.