Hi Kevin
Worst case, no load, will be 1.414 X 350 volts or about 495 volts. Your capacitors should never see this voltage as most radios have some resistors to ground and the rectifier tube has a voltage drop. Also if the radio has a slow heating rectifier, such as 84, the voltage will not be as high since the other tubes in the radio will be warming up at the same time, drawing current.
If you are not sure, to be on the safe side, AES does sell 10 mfd @ 500 volt electrolytics.
Norm