If I were going to do the conversion I would :
(1) Purchase a new compressor designed for R134a, verify it is filled with the right amount of oil before I install it.
Many folks simply flush the existing compressor and refill with the proper synthetic refrigerant oil. But all the rubber parts, like the shaft seals, are not compatible with R134a. Plus lets face it, that old York compressor is an old soldier. It has to be retired sometime. Its bound to be a leaker.
(2) If the new compressor requires different fittings I'd replace the hoses with new barrier hoses having the correct fittings for the R134a compatible compressor. However, if the new compressor IS compatible with the fittings on the original hoses then I would simply disconnect all hoses at both ends and flush them with solvent, blow them dry with air. I'd repeat this as often as necessary until I was confident the hoses were clean and dry.
(3) Flush the evaporator and condenser the same way.
(4) Replace the receiver/drier tank. This is something I was taught to do every time I break-open a refrigerant system.
(5) Replace the O-rings at all the fittings with R134a compatible O-rings.
(6) Folks in the refrigeration business say installing a high pressure switch is a good idea, so I'd do that next.
(7) Most R134a conversion kits don't have replacement expansion valves. People seem to get away with their conversions without replacing it. I'm not qualified or experienced enough to say it must be replaced, or not. I'm not saying replacing it isn't a good idea either. I'm just saying that a lot of people perform the conversion using the OEM R12 valve. However, if the replacement expansion valve is readily available, if it is a direct "bolt-on" swap that doesn't require changing fittings, and if the price is reasonable … I'd most likely say to myself "heck why not".
(8) Evacuate the system with a vacuum pump for at least 24 hours.
(9) Fill the system with ≅ 80% of what was required for R12. If memory serves me correctly I think 80% is the right number.