Don't worry. You won't break your amp. Mesa spec, when referring to tubes for use in a Mesa, means that the plate voltage of said tube needs to be within the optimum range for the right amount of breakup to occur. If the tube's plate voltage is too low the amp will sound thin and 'nasty'. If it is too high then the amp will have too much breakup and sound bad as well. If anything the tube life will be reduced if it is not within Mesa spec but you will not harm the amp.
Groove Tubes uses a scale of 1 - 10 for the 'hardness' or distortion rating for their tubes. The GT tubes that are within Mesa spec have a rating between 4 and 6. For other tubes I just make sure I tell the place I order my tubes from that I have a Mesa and they make sure the tubes are within spec.
HTH