They don't have to be dimmers at all. Did you have a specific relay in mind?
Looks like I shot my mouth off without reading your post closely enough. I'd thought the heatsink was interfering. Your post indicates it's the body of the switch that's hitting the corner radius of the box. Switching to a HAI relay won't fix that (body size is the same). Switching to another brand might give you a more generous radius on the switch corner, but I'm not that familiar with the UPB line.
Just to be clear - these are 600W HAI UPB switches (4.1" x 1.75" x 1.45") - correct.
I've never had a problem fitting a 1.75" wide switch(s) into a box (plastic, composite, or metal). - depth yes, width no. If the interference is minor, and you have enough material in the corner, I might consider squaring the box corner up with a flat file. For the amount of work involved (sweat), it might be better to just dice out the old box and install a retrofit (as others have suggested).
Sorry for jumping without reading,
IM