I would think the Thomas rule (that time is money) would apply equally here. If you report as LT you pay 15% perhaps on the gain. If you report as ST you pay perhaps 24% so the difference is 9% on $17.
Are the dates you are seeing on the 1099B? I’m a bit surprised because
I had a similar situation (different securities) with a small CIL caused by selling a fractional share from a merger/spinoff. I think the acquisition date may not be correct since there were several such transactions over the yrs but they took an acquisition date from a prior spinoff and that one was long term……..maybe because it was covered at the time.
I wonder if the fact that cost basis is unknown by itself implies a LT transaction since otherwise broker should know the basis? I guess I would report as LT and let IRS decide if they wanted to spend the time & effort to possibly gain 2 bucks.