If you are not filing a claim for your damages through your collision coverage then a deductible would not be need to be paid.

The other party's damages should be covered under your property damage liability portion of your policy which does not have a deductible amount for you to pay normally.

Keep in mind if you choose to not repair the damages to your vehicle at all and are later in an accident where you would file a claim for damages these pre-existing damages may affect that claim. An insurance company would be able to deduct the amount of the pre-existing damages if the new damages were in the same area of the car. Or if the car was totaled out the previous damage the car sustained and did not have repaired would affect the actual cash value of the car.