On my '90 Prelude Si it was super easy, just undid the cover over the rear-view mirror mount (mounted to ceiling, not windshield), unplugged the unit that made the sounds as well as lit up the seatbelt reminders, and it was fixed.

If you can find the location of the sound-maker unit(s), you could just remove it. Otherwise, on some cars you can remove the interior light fuse and it also disables the reminder noises - what I've done on my 5th gen civic in the past - otherwise there might be another fuse that will accomplish it.