Get yourself a nice black rat snake.
(Unironically, it drives me up a wall when I hear about people trying to exterminate snakes and spiders; the only reason those are around is because their food is.)
> the only reason those are around is because their food is
For some reason everybody in my city is proudly boasting bout the recent large capybara population... And again, for some reason those same people didn't react well when jaguars decided to show up in the urban area.
I wouldn't worry about them. A few thousand people get bit by them every year but there hasn't been a fatality in decades. They're very unlikely to bite and very unlikely to cause any harm at all even if they do bite.
Rats are brilliant animals, they’re just tiny dogs. If you treat your rats well, they would have no reason to attack mice and would co-exist (although your rats would probably get sick because of disease. Pet rats (fancy rats) are illness prone.)