How can I install a dishwasher under a 23 inch deep counter space?
You can definitely get dishwashers that are not as deep as the standard, though selection will be more limited.

One thing to consider is that the dishwasher needs a bit of clearance and wiggle room, so you'll likely need to accomodate more than 1" difference.

I would recommend against chipping away at the studs in you wall as this will reduce the strength of the studs and wall significantly.  If this is an internal non-load bearing wall this might be OK but this would be a big problem if it were a load bearing wall.

I think the best/easiest solution is just to find a different dishwasher that will fit your space.