Nice job a number of us have done similar installs for the exact same reason, "funky clunky plastic pull". I would suggest that you install some insulation on hte back of the cabinet on outside wall and around and on the outside shower fitting, unless you are going to chill your wine in that cabinet.
I like your reconfigure for usage.
SEE this for the insulation suggestion. Not bragging just showing what i did. Look for the black sink drain trap, that is right in fornt of my outside shower compartment.
insulationAgain good thinking nice job.