When I was building new houses, I used the fans mounted on the outside wall. Duct ran straight from the custom made hood to the motor outside the wall. Inside the cabinets the duct ran through, the duct was boxed in against the back of the cabinet and finished like the rest of the cabinet interior. No buyer ever said anything about it one way or the other.
The ducts are really easy to clean out. You take the filter out of the hood, and you can see right to the fan. I had a local sheet metal guy that I went to High School with make the liner for the hoods for me to my measurements.
I was building everything about the houses, including the cabinets, so there was really no problem at all for me.
I can't find the exact fan I used, bought from a local supplier, but they were something like this, although backdraft damper was built into the fan unit. Variable speed, and they looked a little better than this one.
https://www.supplyhouse.com/Fantech-...ct-Fan-116-CFM