Back to the opening question, don't think the chihuahua would win.
Had to rescue a little dog from the fury and anxiety of my cats yesterday, in my own garden btw. Don't know what his state would have been like if I had not intervened. He escaped from his owner, straight from the dog-trimmer. And got cornered in my front yard.
He did not look clean anymore, but he was still in one piece. He lost a bit more fur than intended though. White clouds where everywhere.