That's a pretty good price. We don't know if your in the US. Radio Shack should have something as well.
Remember that a project has a lot more than a switch:
Some other possibilities.
switch
Case
Feet
Solder
Soldering Iron
Wire
Grommets
Fork terminals/Binding posts (attach to speaker)
Wire nuts
I might envision a box with a switch and 3 grommets entering on one side. One goes to the radio, one to the kitchen speaker and 1 to the den speaker. Each wire would have an Underwriter's knot tied in it to prevent the wire from being pulled out.
In the box, I might have just pieces of wire to the switch and would wirenut everything inside the box.
I have no idea how your speakers connect, old and new nor do I know how the connections to the amp.
Way back when I could say screw terminals on the amp and wires on the speakers.
Then it was binding posts on the amp and binding posts on the speakers.
Then it was RCA plugs on the speakers.
Then sub miniature plugs
Then for the high end stuff Speak On connectors on the speakers.
I've seen speakers with a combo RCA/screw terminals.
Connectors are a possibility. There is just so many ways I could envision.
You could also do a nice job using external DIN terminals with wire protectors or DIN terminals without protectors/or with protectors with wire ferrules.
www.Jameco.com would probably have what you need from boxes to single feet.
Your hookup is "somewhat special". If you used a 4PDT switch, then connections are less critical because of 4 separate paths.
e.g. Like the 7001 switch in this datasheet:
https://www.electro-tech-online.com/custompdfs/2012/01/70128142.pdf
Price is about $13.00 w/o shipping. Note pictures don;t match item which is typical. You have to consult the datasheet,