I wouldn't replace the cover plate. Id bury the entire switch in the wall. Concrete is not difficult to drill, and breaks quite easily after being drillled enough. You only need an inch deep for a light switch and backbox. Replace this monstrosity with an ordinary flush surface switch.
A comment asks what about risk of impacting integrity, especially as its a basement.It also asks about making a trench for the cable too. I'll comment on this below.
Good question but almost guaranteed zero risk.
It may be structural but that wall appears to be concrete block. Or if not, then it surely will be 100-150mm (4 - 6 inch) thickness, maybe more. In either case a 25mm (1 inch) backbox, will be no problem at all. There (probably) isnt such a thing as a concrete wall of this kind for a basement/cellar, where a backbox cutout or shallower conduit cutout would compromise waterproofing or structural strength. It's virtually impossible to imagine that being the case.
- Because it would imply a shockingly thin wall under 50mm thick, below ground. Which would crack and leak, and not be sufficient anyway.
- Because being an internal wall the design must anticipate screws and plastic plugs for them (or other wall fixings) being drilled/cutout anywhere, up to 50mm (2 inches) deep, already, as part of the design. One example being the hidden screws almost certainly holding the existing monstrosity to the wall....... :)
As for the cable, personally I'd bury it, but surface mount is an option.
If the OP is still truly nervous, one could bury the backbox and surface conduit the cable, or get a low profile surface box instead.
For burying, I'd suggest thin stainless steel tube/box section 15x8mm with 0.5-1mm wall off EBay (or shower rail tube from local shop!), as conduit, and a thin cement/mortar cover, to match rest of wall and protect the shallow buried cable. Stainless as below ground. Take care to seal any embedded electrics well on all sides, with a builders low modulus silicone mastic against water intrusion reaching the conduit and/or backbox, as it's below ground,if there is any risk. Or if not, surface mount a cable or low profile conduit, and a shallow surface mounted box.
But that monstrosity is better replaced than fixed, and probably cheaper to do so as well.