I do these restorations for my own radios. In restoring the Hammarlund HQ-129-X I replaced ALL of the condensers, checked all of the resistors, replaced any that had drifted out of spec with new 1% resistors of equal or higher wattage, tested and replaced any weak or bad tubes, and did a complete alignment which is somewhat tricky because of the crystal filter, which requires the IF to be aligned to the actual crystal frequency which always varies slightly from the listed IF frequency slightly, and requires special gear to determine the frequency, or using an alternate, much more time consuming method which few techs today would know. After that I had to strip the cabinet of layers of hideous old paint applied by various owners in past years, and then re-paint the cabinet. I enjoy doing this work for myself because if worst came to worst it would only be my own property that would be screwed up, but I would not want to do this work for a stranger.
Before:
After :
As for your radio, a radio of that vintage will require all of the above to be reliable and work to its best. One might get away with replacing only the power supply filter condensers at a minimum, but that would run the risk of other condensers failing soon and causing damage to the circuitry, which is why a proper restoration requires all the above work.