The car alarm type would work just fine if you found one that fit.
That's odd if there is actually a pushbutton - most home alarms use magnetic sensors. There's a magnet attached to the door, and a magnetic switch attached to the frame.
Radio shack should carry them, otherwise try a home depot/lowes, or look online - I'm not positive but
www.partsexpress.com might cary some home alarm parts.
It's definitely not a complicated item, you shouldn't pay more than $4.99.
Edit: the one piece of info you'll need to know is if it is Normally Closed or Normally Open. (the circuit) So what you can do is simply cut the 2 wires going to the switch. (that's "open") See if the alarm thinks that means the door is open or closed, and work from there. For instance, with the two wires cut, let's say it thinks the door is ajar. That means that the switch in its resting point is "normally open." When the door closes and pushes in the switch, contact is made inside and the circuit is closed.