Not sure if your wheel has the usual cracks or not and if they require repair... But if its just a freshen up, consider buffing and polishing it using very fine grit buffing and rubbing compounds. A light touch with some wax and elbow grease just might give it the polish it needs.
I find that rattle can lacquers and off the shelf enamels wear off in places like that.
For small change you can always get a half pint of a good two part enamel for little money. Mix the hardener and enamel with a tiny bit of reducer and use a disposable spray bottle.
If there's a local body shop ask them if they have any leftover enamel, mix with reducer there, and add some hardener when you're ready to paint at your place.
I have also used POR 15 chassis black on my tractor steering wheel that sits outside year-after-year. It's holding up too.
