Is it clever to polish non aluminium parts?

Previously wrote:

The original finish would have been cadmium plating which is quite soft. This is often scraped off when removing the spindle. Polishing to the extent you have has probably reduced the diameter of the spindle by a couple of thousanths of an inch. That shouldn't be a problem. A good plater should be able to Chrome plate just the larger diameter for you. Copper plate followed by nickel and then chrome for the best result.

So if you want to improve the finish on a 41 year old cadmium plated part, is there really any alternative to re-chroming (apart from replacing the part with a new one). Here in Sweden chroming is seriously expensive and on top of that it typically takes 4 to 6 months to get the part chromed.

I would not worry about it. Make it look good, put the bike together and have fun riding it. It will not corrode badly unless you neglect it again or get it wet regularly. Just try to keep it dry as much as possible and maybe wipe it down with penetrating oil now and then.

In the days of Knights and their armor suits, they polished the bare steel to a mirror finish, this way the grain of the metal was burnished and sealed and actually was much more corrosion resistant than non-polished steel.

So there is not right or wrong thing to do here, just do what makes you happy. The only thing I would check would be your wheel bearings. I had an old Norton that had been stored for a few decades and I rode it pretty much as it was, which was sort of scruffy looking, but I did find a bad wheel bearing in it despite it only having 5000 miles on the odometer. I replaced them all for safety's sake, as I often took the bike up to 100 mph and certainly did not need any problems or surprises at those times....