If that's you spare replacements, I would suggest to try taking one of these smaller switches apart before you work on the one in the unit.
. First remove the spring from the shaft lift the end of the spring to outside of the larger white knob backing plate. Now rotate the spring and it will unthread off of the front of the shaft. That spring is one of the things that hold that white plastic cover on top ot the switch. See if it will now come off the top easily. If not then you need to desolder the contact cleanly using solder wick, so that all contacts are free. Now Bend the metal tabs holding the switch to be removed from the assembly (Near the white plastic top cover). Now that cap should come off. And then I believe the shaft will pull out from the front.
But if you have spare slide switches with the right contact config, just replace the switch (Unsolder, and bend to tabs to allow switch to be removed from the top. You houldn't need to remove the spring, but may need to push it forward to get it off the tab that holds it in place on the metal bar.
Those shafts are made of a nylon type of material, and pretty hard to glue, although JB weld is the best to try with. But I would either use a Dremel drill, very small bit, and drill into both sides making a hole that you can use a length of straight pin as a shaft to hold together, JB weld the pin in, and the broken sides. Another way is to get a pin real hot, use it to make a hole in both sides, and then cut the pin shaft to a length to use to reinforce the shaft, using JB weld as above. Extreme care must be taken with both methods.