Update from the original listing!
The original matching Sho (or short sword) was found, completing the Daisho. There is a video of the New York Japanese Sword Exhibition - Azuma Galleries in 1995 that shows the Daisho being together at 1:42 of this video https://www.youtube.com/watch?v=rt5Kdb3A52c (see video below).
In the video, it is mentioned that many Daisho sets were broken up over the ages, so it is quite remarkable that they have been reunited.
Katana is unsigned most likely from the late Koto period. This sword has a hamon of suguha (a bit difficult to see due to its old polish). The jigane is a nagare itame with some masame. There are a few Kizu, and what looks like a sword cut on one side. The tang is ubu, but with 4 holes (1 being a shinobi ana).
The Sho is a Shinto wakizashi with a hamon of gunome ni notare. The nioi guchi is done in a very fine fashion made up of ko nie and nioi. Ashi appear through the hamon,. The jigane is a well mixed itame with chikei. There is some small openings in the ji and a small fukure on one side. The boshi is healthy done in a chu maru fashion. The blade has been cut down several times, thus losing its signature.
What is nice about this set, is the Daisho koshirae. The tsuka are lacquered over ito with silver fittings. There is a special type mekugi (see pictures) with the matching mon on the fuchi of the 3 Oak leaves favored by the Tosa Yamanouchi family. On the Dai saya, the hanger fittings are a type seen in the late shinshinto period in which the sword can be worn as a katana or a Tachi. The hanger actually split apart when it is worn as a Tachi. The aogai scabbards is very nice and in good condition. The tsuba are a Nanban Hizen type with nunome zogan as well.
The 2nd katana mount is for Iai, made up of modern fittings.