The alarm is hard wired into the main wiring loom at the factory, I can't see how you can just get rid of it.
Have you tried the Alarm resetting sequence for your year of car, outlined in the FAQ
Just for extra info, I currently have my mothers Toyota sitting outside the house. The keyfob sets the alarm and locks the doors as it should. But after a random period of time the alarm will suddenly and for no apparent reason go off.
All doors locked, no wind, and no-one within 500yds.
Annoying to say the least.
However it turned out to be a very slightly badly positioned door seal allowing the doors to lock etc but when things relaxed there was just enough movement in the door to fire the alarm.
This was discovered by having someone lock me in the car from the outside and then me pushing on each door from inside until the alarm fired.
Just a thought.
Also try simply locking the doors by turning the key and not using the fob.