Bathroom cabinets - help!

[Fivefootoffun]

The units in our downstairs toilet have started to peel - due to a dodgy seal apparently.
I had hoped to just be able to replace the units and leave everything else in tact (as the work tops match the tiles and I’m not mad about them but not in a position to do a full bathroom refit just now). The bathroom company we had out said it would all need to come out.

anyone got any ideas for a cosmetic fix? I wondered about wood filler then sanding then painting over but I’ve no idea -
would that work? Quite a few spray door companies round here - was thinking of giving them a call but thought would check on here first.

thanks in advance for any wisdom 🙂

Sorry here are pics!

Sorry, this isn't a wise response (and I'm sure somebody will be along with a better idea), but maybe you could stick some laminate border tape or trim on the edges just to tidy - maybe a silver metallic edge or something with a gentle pattern if you can't match the existing colour?
Internet does also suggest hot iron fix for peeling veneers.

Thanks so much - I didn’t know such a thing even existed! Off to google it - much appreciated. It’s really just to tide is over until we can get a new bathroom so would be ideal. Thanks a lot!