You could do what the cowboys who renovated my place, before I bought it, did:
just glue new tiles over the top of the old ones.
Tile over tile is an acceptable practice as long as the originals are stuck on well in the 1st place. Only cowboy territory if done badly or planned badly. Ie. I’d not over tile half height as you’ll see 2 thickness on the top edge.
You might get lucky and find it was painted before tiling, that way they should come off fairly easy, even on plasterboard. Stick a thin blade down the back and give it a little pull, if you see movement it might be your lucky day. Any remaining tile adhesive can be scraped off after using a wall paper stripper to soften 1st. Prep and paint, job jobbed.
The cladding idea works well, but would need the sanitary ware removed to make a decent job of it IMO.