Thanks for all the replies.
I would have kept the sticker, if it's corners wouldn't be all torn, dirty and crusty - so I removed it. As I first planned, I attacked it with rubbing alcohol (ethyl alcohol with smelly pink additives). It worked like a charm, the sticker peeled right off. There was no damage to the plastic whatsoever.
The meter's front was covered with nasty glue residue, that also came off beautifully with rubbing alcohol.
The real pain in the a** was the "calibration void if torn" sticker over the CAL switch on the front. I spent at least 20 minutes slowly chipping the pieces, as the sticker was so fragile, it was impossible to remove otherwise.
Alcohol didn't help at all in this case.
Anyhow, the meter looks great now, I just need to find it some feet (the unit was probably rack mounted before - the side screw covers are missing as well).
I have attached the picture of the area, where the two stickers used to reside. Squeaky clean now.