Absolutely, but I'm not sure what qualifies as cheap. You will have to get to Bethel, pay for air taxi and possibly raft rentals, so cheap is probably $2K per person.
A few google searches for Kanektok DIY or Kanektok raft trips will turn up quite a few people who have done it and descriptions of their trip. The DIY trip is from the lake down, 7-10 days. I don't think there are any lower river only options as that would require a jet boat. Papa Bear Adventures out of Bethel provides air service and their website also has descriptions of the trip. I recall there being some good descriptions on the Alaska forum Outdoors Directory.