Just a small update on this for anyone who might be having similar issues in future:

Fuse 35 is fine. The other things controlled by that fuse (instrument lights etc.) were all fine. I replaced the fuse just in case (because hell, why not!) but no joy.

I took the hazard switch out of the SLK and it's identical in form-factor to the Crossfire hazard switch. I haven't taken the Crossfire hazard switch out yet as it's a job for the daylight hours but the only difference with the two switches is going to be the fascias for the lock and ASR (traction control) buttons. On the SLK switch I have here those fascias are held on by two 'indent' type tabs so they're very easily popped off.

Assuming that the Crossfire button fascias are the exact same, which is almost certainly the case, then I can just swap the fascias from the Crossfire hazard switch over to this one and I won't need to buy another switch at all.

Fingers crossed that fitting the replacement switch will resolve the issue!