Absolutely. I've come across a few mom and pop shops selling beautiful knives. I liken it to some of the famous blues artists like R.L. Burnside who were completely unknown till someone with a camera spread the word. If it is a quality piece don't worry abou the brand.
In Kyoto most itineraries being people to Nijo castle. You can conveniently check out 2 shops that are only a few blocks away. The first is Shigeharu. He makes nice knives. Some interesting pieces in stainless clad Aogami Super too. Another shop is Yasushige which is very close to Shigeharu. These are two shops that are known within the knife community but as they have no distribution, etc. you'll hardly ever see them outside Japan. They don't see a lot of tourists either.
As for the tuna auction it is good that you are only a few blocks away because there is no public transportation that early. Beware that you will have to arrive closer to 4am for the auction. You'll have to stand in line for tickets and there are a limited number. Take the opportunity to wander the outer market for breakfast after the auction. There are a bunch of shops selling the best sushi and sashimi in the world.