It's not a run cap, too low in value. It's most likely just to suppress arcing across the motor's on/off switch. I replaced similar one in my Thorens.
For a modern replacement I use 275VAC X2 film cap. It is subject to mains transients when the TT is off, hence the high voltage rating. But if it fails short circuit no fire hazard or anything, because it's in series with the motor (when the switch is off).
So I would say your 630V part is fine, if it fits.