Thanks for the input.
Can either of you recommend a switch? I am pretty electronically challenged.
Remember, this is entirely optional -- if you aren't concerned with both the 4 way and 8 way being active at the same time, this is completely unnecessary.
If you decide you want to do this, you have a fairly wide selection of switches to choose from that would all work. What you want is a SPDT switch (single pole, double throw), much like the microswitches used in arcade buttons, where there is one common connection and two other contacts. In the case of the microswitches, one of those contacts is connected to the common (the one you connect to ground) when the button is NOT pressed and the other connects to common when it IS pushed. However, for something like this, you don't want a 'momentary' switch - that is, as soon as you release the button, it returns to it's normal state.
So, the long and short of that is that it depends on what you want. However, a rocker switch, a slide switch, or a pushbutton switch that is NOT momentary would work fine. Just make sure to get SPDT. I'd recommend browing Radio Shack or similar and picking one you like...
In case you're wondering about wiring, here's a simple diagram that shows how to run the grounds through a switch and to both joysticks. It shows ground wires only -- you'd connect the wires from the normally open (NO) contact to your keyboard encoder as usual.

Hope that helps.
-LakeShark