As an Auto Painter I can tell you how I would do it. I do have the convenience of color matching the rim myself with PPG Omni Mtx
I imagine the rim is gloss or somewhat close. If not full gloss I do have a flattening agent to add in ratio.
In your case your best bet as mentioned is to take it to an auto supply store and have it color matched. They will probably not want to sell you less than a pint but maybe you can get a special offer. The problem with applying only basecoat is that it is very thin, flat and less durable.. It is designed for another stage which is clearcoat .
I would spray it with the single stage gloss paint and slightly flattened if need be. The Omni mtx I have for example is a 4

2 mix. Paint, hardener, reducer.
So this should be considered as part of cost as most paints have mixing requirements. Even basecoat is mixed up to 100% with reducer.
But if you want to just get paint and brush it on that's up to you.
I would apply 2 coats. The way I would do it as I imagine the rim is marred all the way around at the edge would be to back tape the lip off by applying a feather edged tape to prevent a hard edge being formed and spray the entire outer lip. With just 2 coats after pulling the tape very little to no mark would be seen.
pollo