Passing plumbing through a wall.
Dishwashers don't require a full size drain. There is no need to run a DWV line to your dishwasher.

They drain through a 5/8" or 7/8" flexible hose that attaches to the sink tail piece or the food disposal unit.

They fill through a 1/2" feed line.

You shouldn't need larger than a 1 ½" hole through the wall into your cabinetry and then run the lines in the back of your cabinets. I think you will want to go lower though since your drawers probably go all the way to the back of the cabinets and anything mounted there would keep them from closing.

Have you bought the DW unit? If you have it, check the install instructions and the feed and drain line sizes.