For the output cap, the capacitance is not that important. The problem is that with old caps the ESR often goes up, and this could lead to instabilities. The circuit might need some ESR for stability, but not too much. To be on the safe side I would replace the output cap. My choice would be something like a normal (that is higher ESR) 220 µF in parallel with a low ESR 220 µF.
For the large main filter cap, I would keep it - the large ones tend to age less, as the liquid to seal area ratio is higher. At least this would not be the first priority.
With 35 V main filter cap, there should not be 50-60 V at the output !
What is the rating on that supply ?
The first test should be done with no load or a small load (e.g. 1 K), to reduce the risk of further damage.