It's hard to tell how much space you have from that image - it looks like plenty of room but you say it would hit the DW. (Is the DW between the sink and radiator?) Do you have a 2 dimensional overview with dimensions marked? In any case, if you get a French door model, the doors will be narrower and could give you more options.

and if you want the hinge on the right hand side (next to the cabinets) you will need a SPACER for the door to open all the way.

chicagoans, a French door model will be too wide for us. We have maximum 31-32 inches of space for a counter-depth fridge.

M Miller - we're considering Fisher Paykel counter depth 17.5 cu ft. The door next to the fridge is now actually just a doorless entry into a mudroom.

new-beginning - what is a spacer and why would we need it for the door to open all the way?

Consider a 30" counter-depth with the hinge on the left. That may miss the dw.

Spacer: in this case, a piece of wood that matches the cabinets that will go between the last cabinet and the fridge. Usually you use spacers between cabinets when the length of the wall doesn't exactly match the summation of the widths of the cabinets. In your case, you have to make sure you have enough space to the right in order for the door to swing fully, else you might not be able to pull out any drawers. Or you may bash the door against the counter top. For the counter top, you usually round off the corner depending on how much overhang you have.

Counter depth means different things to different manufacturers. For the expensive built-ins, it means exactly counter depth in that the fridge matches the depth of the counters and blends in completely. For the stand-alone units, it usually means that just the carcass is counter depth which can be 24"-27". The doors stick out farther. And how that door swings (function of the hinges) determines how much room you'll need to the side.