Not sure how the female part of the seatbelt is fixed in the cougar.
I'm not an expert, but wires to seats would either be and indicator that someone is sat in the seat so a light on the dash shows for them to put on a seatbelt and without side airbags in the seats I'd have thought the only wiring tied in with the airbag could be a seat belt pre tensioner.
In my spider a had to locate the female part of the seatbelt on to my seats, as they were on the original mr2 seats.
I say disconnect any wiring from the seats and see if you get any dash warning lights when you start the car. No lights, no worries.
It's generally a bit of trial and error when trying something new, mate, but taking the chance can be well worth it. I reckon you'll sort it no problems.
Beany