While I haven't looked specifically at my Windstar's passenger airbag, I've done some research in this area (I'll try to look at my 2000's passenger airbag connections tonight).
There will be a wire connection to the airbag; it should be visible under the dash (but may be difficult to get to due to the glove compartment). Note that many airbag-related electrical connectors I've seen are made of bright orange plastic, just so you know to pay attention to them. If you disconnect the wires going to that airbag, it won't deploy in a collision.
Now - that said - there are a few more issues. The airbag controller will recognize that a connection is missing, and should cause the airbag light to stay on. Yes, I'm sure you can live with the light - but this also means you can't be sure that the driver's side airbag is really operational.
Possible solution to this issue for techy types: Wiring the correct value of resistor in place of the passenger airbag should allow the controller to think the bag is still there. Of course, this also means no one else can determine that the passenger side bag is deactivated, but I'm presuming this isn't an issue based on your description. But this does mean the controller is correctly able to determine that the driver's side bag is in order.
Of course, insert standard disclaimer here: I haven't actually tried this; your mileage may vary. I can't take responsibility for changes you make to your vehicle's safety systems. Do your own research before mucking about with the wires. Etc.
Later edit: Hints for techy types: Google "airbag deactivate resistor"