I expect someone with some CAD skills could create a model of the shaft. I'm no 3D printing expert but perhaps something like nylon or ABS would work and many printers can handle this material. In my case, I had an older Model 169 that I've been unable to repair that I decided to use as a parts donor.
I was unable to find a way to remove the switches from the front. There is a tab sticking out of the rear underside of the shaft for which there is a slot cut in the rear of the housing, but the slot is not present at the front of the housing. I'm unwilling to use the amount of force that would be required to try to jam the shaft into the front of the housing. As a result, I was forced to remove the rear switch interlock rail. That wasn't too difficult except for the fact that I needed to remove a Caddock thin film resistor and a large wire-wound resistor as well. Using a Hakko desoldering iron, the Caddock came out without issue. However, I struggled with the wire-wound resistor for a long time, trying every trick I know to get it out. In the end, I succeeded, but destroyed all of the pads on the underside of the PC board and damaged several of the pads on the top side in the process. Hence my original preference to find an alternative way to replace the shaft.
With the components out of the way, the rail came off the switches without issue and the broken shaft came out the rear easily with a slight push from the front of the housing. I loaded the donor switch assembly with the spring contacts in the original configuration and with a bit of fiddling was able to insert them into the rear of the housing. See the images below:


If I had to do another repair like this, I would sacrifice the 5-legged wirewound resistor in order to avoid any PCB damage -- assuming I could find a replacement. The PCB hole size for the leads have barely enough room to fit them making desoldering them difficult. There just wasn't enough clearance to get all of the solder out of the holes with the leads in place. As it stands, I'm fortunate that only one of the leads of the resistor was connected to a trace on the underside of the board making that an easy repair. Whether it will still be able to handle 10A of current in ammeter mode is uncertain, however.
While I have made no attempt to desolder any of the switches, I would have a big concern about limited clearance to draw out the solder. If the legs of the switches are a tight fit into the holes as they were with the wirewound resistor, I think desoldering them with conventional rework tools would be quite challenging.
Oh, and yes -- the board is a Model 197A. I didn't mention that in the title since this seemed applicable to many of the Keithley models of this era that use these types of switch assemblies.