How hard would it be to hack a "personal soundtrack shirt"
You should be able to use a multimeter (without power) to figure out how the buttons are setup.   

I would guess they are multiplexed, as there are 10 wires, and 6 rows and 4 columns on the keypad. As you can see from the below diagram (of a 4 x 4 matrix), the uC cycles through, setting each column high in turn and checking for a high on any of the inputs. In this example you can see how the press of C3 is detected.  



So assuming this is how it is set up, set your multimeter to continuity test mode and apply the probes to two of the connector pins. Press each button until you hear a beep, note button/contact numbers and move on.
You will soon figure out which pin is connected to which row or column.
When you have done this make your own switch matrix to use for your christmas sweater.

EDIT - For the continuity testing, I meant a multimeter on the ohms range (or the dedicated diode/continuity setting, which beeps when there is a short between the probes)
You are looking for which two lines are shorted when each button is pressed (so the display will show high/infinite resistance until button is pressed at which point it will drop to around zero ohms)

Here are a couple of link describing how to make a button matrix:
Keyboard Matrix
DIY Membrane keypad  

If you don't want to make your own you could buy something like this. Even if you don't buy one, the datasheet from that keypad might be instructive to look at.