I don't think the switch had anything to do with the capacitor. If it had a bulge before then is wasn't going to last much longer. Hopefully the value is still visible on the old one or if your lucky the value is marked on the motor plate
Just a guess but it may be a 65uF capacitor but it does need to be rated for 450 vac. If the capacitor value has been low for a while it may have contributed to the switch failing as the motor could have been taking more current to start/run