Not sure what model # the "original MS BT mouse is, but their 5000 model has a "hardware-managed" mode which would likely need to be triggered by a PC connection first. That could possibly eliminate the need to pair using a passcode.

I'd recommend looking for basic BT connection support on MS's site if you haven't already. Here's the link for the 5000 alternative pairing as described above.

FTR, my BT GPS uses 9999, not sure if anyone uses 1234 at all. Keep stab stabbing away!

HTH