Good on you. I might do the same to mine. I must admit the bloody thing can drive me mad a bit sometimes, especially when I don't put the belt on to check the mail at the end of my 30 metre driveway. Same when I get home at night. I'm not going to put my belt on just to drive to the house. What sort of a gonad does that.Thanks for the suggestion vondiesel, this ended up being the solution I used.
Although, this won't be for most people as the same buzzer that causes the seat belt chime is also for pretty much every other chime the car makes too e.g. turn signal, door ajar, etc. I never cared for these chimes either so I was more than happy to remove the buzzer completely. The job was very easy and straight forward.
1. Set the steering wheel all the way out and down to give you the most space to work with.
2. Remove the instrument cluster cover. The cover isn't bolted down, just pull it towards you and it comes right off. The start button is connected to this so it will need to be unplugged. The fabric will need to be removed as well, it's just hooked onto the cover in around 10 spots.
3. Four bolts hold the IC onto the car, you can't miss em. Then a single plug (this may differ for models with active driving display).
4. No need to fully dissemble the IC (as I did in the pictures) just remove the clear (or white) back cover that gives access to the circuit board.
5. Remove the buzzer (see pictures), it's the little black, cylinder shaped piece marked RMX-12. I grabbed it with pliers and twisted until the glue broke loose.
6. All done, just put everything back together.
This triggered a CEL but it went away after an hour or so; I'm guessing unplugging the IC is what caused the CEL.
Now my little Mazda doesn't make a single annoying buzz or ding.