Just FYI, the rifle itself is considered a 'curio and relic' - your own status as a private seller doesn't matter.
Anyone with a C&R FFL can purchase this rifle from you, and you can ship it direct to them upon receipt of a copy of their license. A C&R holder is a specific class of FFL.
"Q: Is there a specific license that permits a collector to acquire firearms in interstate commerce?
Yes. The person may obtain a collector’s license; however, this license applies only to transactions in curio or relic firearms. The principal advantage of a collector’s license is that a licensed collector can acquire curios or relics in interstate commerce.
[27 CFR 478.41(c), (d), 478.50(b) and 478.93]"
I hope this helps with the sale.