I re-sprayed a 1966 Sun Mass Start bicycle a couple of times in school summer holidays back in the early seventies. It was white with chrome forks, so did not have all the colours in the pic.
I worked on R & D of paints in the nineties, and did some colour matching. Some of the pigments used in paints from the sixties were banned, and it might be difficult to do a colour match to the present colour which may have faded from the original colour.
I recall removing the cotter pins with a wooden block so as not to damage, and painting whilst suspended from the handle of a yard brush having removed the forks. I had rubbed down for several hours with different grades of emery paper, so smooth bare metal, then my brother hand painted the frame with coach paint just before I was about to do it.
I tried for a better finish with a spray can on a subsequent year, but not the same gloss as a factory finish. If I wanted to re-paint the frame of my 1987 Raleigh, still in good order, then I would get it done professionally.