On my 06 you can just disable the chime on the seatbelt without causing the airbag light to come on and also keep the airbag operational. Ford didn't change much in the wiring over the years so I'm sure this it the same for many years. But there is also no censor in either driver or passenger seat on my van, so that seems a bit different to Jay's van.
Just disconnecting the 2pin, 4 pin harness (or 6 pin) under the seat, will cause the airbag light to come on. There are a bunch of connectors under the seat. There is a 2 pin connector just on the drivers seat that's located next to where the female seatbelt clasp bolts to the seat frame. These wires have no other use than to detect when the seatbelt is plugged into it and make the chime go off if the ignition it on, they have nothing to do with the airbag. Unplug that connector, or if you are lazy you can simply cut the wires when the exit the seat and enter the female seatbelt clasp as it's a N/C circuit.
Here is a generic Ford drivers seatbelt tensioner.
There are 2 connectors,
1 is yellow and mounted to the underside of the seat, that is the seatbelt pre-tensioner charge. Don't unplug that.
On my van the other is white (not black as in that pic) and that simply detects if the seatbelt is plugged in. That one is mounted to the pre-tensioner charge. (The tube with the yellow sticker on it)