Friction shifting is the easiest solution.

barcon shifters can easily be mounted on reverse sides with only an aesthetic drawback.

A gripshift could also work on the wrong side, just you'd have to twist it backwards(strong hands may be needed) and the display will be upside down.

Suntour sl-sx00-ch thumb shifters; if dissasembled the guts can be swapped between the left and right sides. however it is meant to index suntour 6speed - can be modified to index shimano 7 but takes work and possibly modification to cassetes spacing...

stem shifters and downtube shifters are already located so close to center that handedness would be irrelevant.

p.s. If I only had one brake, it'd choose the front.
Or is this bike for someone with a disability?