Cross tires on a road frame - Brake caliper question

I’ve got an older road bike that I want to turn into a foul weather bike. I bought some 35mm cross tires to mount up, but they’re a bit too tall and they rub on the underside of my brake calipers (standard Shimano Sora). Being that this isn’t a cross frame, it’s not set up for cantilever brakes. Is there another caliper option I can pursue or am I trying to mate something that’s incompatible?

First you have to look at the frame. Will the tires clear the frame and fork? If so most single pivot brakes have more clearance than dual pivots, but we’re talking millimeters here.

Styrrell