You should have it priced lower than an equivalent vehicle at a dealership. Not being able to take a trade-in is definitely a no-go for many people. However, maybe you could point out in your ad that buyers can get loans to purchase from private parties, and add a link to a local credit union or something? I don't think everyone is aware of this possibility.
Several years ago I sold a car that was only about a year old and the buyer arranged financing, I went to the bank with them, handed over the title and they handed me a cashier's check. Assuming you have the title, it should be pretty easy once you have a willing and qualified buyer.