a 185/60 will fit easily on the back of a sedan with the right size and offset wheel. I had 205/60*13 on the back of my old sedan with lipped gaurds. What size wheels do you have?

Do they scrub only when both side of the axle hit a bump, or when cornering too?

You could 'pump' the gaurds out a bit, if they only just hit. But that could crack paint, which could cost extra in paint repairs.

The other thing you could look at is how much material is left on the mounting face of the wheel that bolts to the hub. It may be possible to have a few mm machined off that mounting face.