Just watch out for abrasives and the solvents in some car wax products and be aware there is probably a thin and crappy enough for mil spec, sprayed on, factory finish on the door hardware. You might think about getting a can of clear coat finish and enhancing it with a couple extra coats before waxing. Under the finish is, one hopes, a decent thickness of metal plating---you don't want to polish through that or all is lost.
I have done a lot of work for galleries over the years including placing and hanging fine art. This wax is a fave product of art restorers and people and was brought to my attention by people who restore art and do gold leaf work and gilding. I am not easily sold but recommend this stuff to clients buying metal sculptures a tad more expensive then your door knob. It holds up well even outside. It is somewhat expensive but a small can of the wax will last you a long time. I used to restore antique homes and relied on it after I polished brass, bronze and so forth for the houses.
Minding my comment about solvents that suspend waxes, a huge can of good old fashioned bowling alley wax might be a choice also. You might have to take up bowling to find some though. It seems harder and harder to find.
Remember that whatever product you choose? It is door hardware you are protecting and you will abrade and wear whatever finish and wax you put on off over time. Be sure and add re-waxing and recoating to your maintenance schedule. You do have one written down right? Every household should as a reminder.