If you don't mind the sink cabinet being open when the dishwasher is running, how about adding a faucet and hose under the sink? Then you don't have to cut a hole in the sink top or countertop (depending on what you have).
The plumbing changes under the sink should not be too difficult. Although sometimes you need to be a contortionist to work in there.

I'm assuming there is an extra hole in the sink that isn't being used.

Since you are just connecting to the dishwasher you should only need hot water and a drain. I wonder if you could find a faucet for one of the under counter instant hot water system that would work with your dishwasher. If not try and find a faucet that will work that only takes one hole. If you only connect the hot water to the second faucet cap the cold water inlet so it doesn't leak if you turn the faucet to warm.

Unless the hot water shutoff valve under the sink already has a second output that is capped you would either need to install a tee on the hot water line to the faucet or replace the valve. Installing the tee would be easier.