The uno shade will rest above the switch? If so that should work. You don’t need electrical tape to wrap around the socket. Use any tape. I found gold tape and used it for a similar project.

Yes the shade is above the switch. Sorry I should have backed up more for the pics.

Thanks for the tip on the tape. I have the same situation on lamps at the beach condo (lamps came w/ the condo, bought new shades w/ that same fitting, didn't return because I had such a hard time finding nice white ones that weren't too expensive and fit the lamps). I also need to re-wire one because it has started blowing bulbs so it now sits unplugged.

For future reference, you can unscrew the socket assembly before you wire it up and remove the harp support If you don't need it.