I think everyone has to deal with this... I have an acoustic piano, my piano teacher's piano feels pretty much like mine... but I've had exams on pianos that were incredibly heavy I still haven't figured out how to adjust properly, but it's getting better.
If possible, it's best to practise on your exam piano. I know for me, I didn't/ don't have that option, so I just practise on a bunch of different pianos to learn how to adjust.
I think examiners may understand a bit. During my last exam, my examiner was playing my ear tests and he remarked "wow it's hard to do this on this piano".
Just play your best, and I'm sure you'll still do well. Don't worry about it too much!
PS:For my last exam, the notes I played wouldn't sound if I pressed the key and changed the pedal at the same time... Can anyone explain this?