Have you got the master code, its a bitch to enter but get you into the programming mode and should be able to turn down the chirps. Mine chirps on arm and dis-arm but no louder than any other car.
The brain is spliced into you main harness so complete removal could be a pain. You could bridge it out easily but not sure it that would give you back the remote central locking from the key.
If you really want to quieten it down a bit until you decide what to do then stuff a rag in the siren and point it towards the bulk head.
In the end tho I think a trip to an auto electrician is in order if you don't want to remove it yourself. If you buy a new alarm from an installer they will normally remove the old system as part of the job, might be more cost effective.