Stick the new capacitor in. If this is an axial cap, orient it so the polarity and uF/voltage values are visible, not underneath it. Dress the leads so it doesn't fall out of the PCB. Don't solder it; move to the next. Do this for every cap, so you have a PCB full of loose rattley parts in what you hope are the right positions and orientations.
Here are two caps -- upper is the original, lower is the replacement. Both are 47uF 50v, so the new one is the correct part. Into the board it goes.
Modern caps tend to be much smaller than vintage ones.