Mira 415. Hot and cold feeds reversed?

I am about to replace the 902.55 cartridge in my Mira 415 shower mixer and have recently realised that the original installer has got the hot and cold feeds on the wrong sides, the cold input of the cartridge has been getting fed from the hot supply.

When I install the new cartridge would it be OK to invert the cartridge and the cover with the four screws to correct this, or do I need to swap the pipe work?

The pipes are a pain to get to as it would mean dismantling half the bathroom to access them.