Yep, the SX-62 is a fine SWL radio, I use a pair regularly and also have a SX-42. They are certainly fun to recap!
I wouldnt even take a chance with a variac until the buried caps under the bandswitch are changed plus any associated with the audio stages, along with the electrolytics. B+ goes thru the bandswitch with the bypass on the other side and you just dont want to have to replace a fried wafer.
The 42/62 are notorious for taking out the power and audio transformers due to leaky eletrolytic and paper caps, if they are good then so is likely the choke...OTOH...
After a couple of dozen overhauls of both models combined Ive pretty much seen it all with those beasts
Carl