What can you do? - keep them within your house or garden boundary. I've never let my dog $h1t all over my neighbours garden!
My wife contracted toxoplasmosis from cat crap in our garden whilst carrying my eldest daughter, I have never owned a cat. My daughter had to undergo weekly blood tests for the 1st 6months of her life.
I am a sensible and responsible airgun owner and would never, ever condone shooting a cat - but I certainly do not restrain my dogs from chasing them down once they are in my garden, because after all that's what comes natural to a dog. Just like roaming free comes naturally to a cat.
I know this post will upset a few, but I'm sure there will be plenty that silently agree.
And by the way, I completely agree with needing a license for air rifle ownership - a correct and practical way of implementing it just needs to be worked out.