Brisbane

I don't think you're using "stray" the way most people do.

If it's a stray, it doesn't have an owner to keep it indoors.

If you're dealing with a pet that's been allowed to roam, I'd recommend contacting your local Council for their advice on what to do. I've heard stories of Council giving out cat traps for people to use to catch cats on their property.

If I see it again, you won’t see it again

I mean, if it's got someone to see it, then after it goes to the pound they'll probably just...contact the owners and return it. Might be a fee or something, not sure. Taking the cat to the pound doesn't necessarily mean the owner will never see it again. The shock of having to do that though should hopefully be enough to get them to keep their pet indoors.