Assuming that this is the rifle concerned, see:-

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It appears to be in excellent condition for its age, its serial no of No.1. always grabs a collectors attention. The calibre is really immaterial to a collector and this is a collectors rifle. I cannot see a shooter buying it to use in competition or a re-enactor buying it simply to shoot blanks. It is also (allegedly) factory engraved and as there were only 25 of this model rifle made merely adds to the value. 
As always in the collecting field, rarity, condition, and engraving and provenance, all add up. Whilst most would baulk at the expected price of 10,000-16,000 bucks, that wouldn't deter a serious collector with a bulging wallet from purchasing it. I know of two Sharps Borchardt Long Range rifles that brought over 55,000 bucks at auction and there were a lot more made than this model Wesson. The final answer is always down to what someone is willing to pay on the day. There may not be a bid or it could go for much more than the anticipated price if two or more collectors are fighting over it. Just my two pence worth.
Harry

You probably will only see one for sale every few years. If you collected them and wanted one I would buy it at that price. I wouldn't buy it as an "investment". Antique guns bring a lot more than they did 30years ago but a lot less than they did 7 or 8 years ago. Sharps rifles I wanted to buy in 2007 are being sold today for 15-30% less now then they were back then.