Here are some handy links about OH firearms laws.
http://www.nraila.org/statelawpdfs/OHSL.pdf
http://www.buckeyefirearms.org/Ohio-Gun-Laws
I'm not an expert on OH firearms law, but it seems from reading those documents that private person-to-person sales to other OH residents are legal under state law. No license is required except to carry a concealed handgun. Speaking of which, it's common practice to vet potential private buyers by asking to see a valid concealed handgun license. If the person has one, they've already passed a stringent background check.
It's illegal under federal law to sell a handgun to residents of other states who don't hold a Federal Firearms License (FFL). An 01 "Dealer" FFL is required to operate a business selling firearms, so these are the most common type of FFL you'll encounter. Be aware, however, that not all out-of-state FFLs will accept firearms from out-of-state private buyers; there's not necessarily a legal penalty, they just don't want to get stuck holding the bag if the gun turns out to be stolen or illegally modified. Usually, if you want to sell a gun across state lines, you'll give it to your local FFL dealer, who will then send it to the out-of-state FFL. This is known as a transfer, and most FFLs charge a fee- typically $15-$40- for this service.
There's another type of FFL known as an 03 "Collector" or "Curio & Relic" (C&R) license, which is intended for private individuals who collect old guns. This type of FFL gives an individual the same interstate buying privileges as a dealer, but only for guns that are either >50 years old or appear on a published ATF list. If the gun's estimated age is correct, it's quite possible that your wife's Colt is C&R eligible, greatly increasing the number of potential buyers.
I recommend posting pictures, information, and a serial number in the "Revolver" or "Curio & Relic" subforum to get a definitive production date. (For privacy reasons, many people blank out the last few digits of their gun's serial number with x's, i.e. "C1234xx".)