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 strenght 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.