Alarm goes off after opening door

Here's the wiring diagram for the alarm system. If you don't mind it not working, the easiest thing to do is just cut the wire to the noise maker.

Ford Service Manuals - Wiring Diagrams

Comparing the two wiring diagrams one gets the impression that the alarm sounder is separate from the regular horns. Perhaps this is not the case?? Don’t have a factory alarm on mine to actually look at. Definitely don't cut your regular horns. Here’s the wiring diagram for the regular horns to compare to the alarm wiring diagram:

Ford Service Manuals - Wiring Diagrams

Ford Service Manuals - Wiring Diagrams

Note the black/light green wire to the "Anti-Theft Horn" while the regular horns indicate a yellow/light green wire. The regular horns should have some kind of quick disconnects on them. Just unplug them and set off the alarm to see if they're what the alarm uses.