Spike is right. Don't worry. You should be able to use your original wires as they can be easily disconnected - see photo.
I can't see an airbag igniter wire if it's cut or not ( should be ended with a yellow plug). If it is you will have to replace it with the original one taken from your car. Soldering is a bad idea.
In order to replace it anyway the side airbag will have to be removed. I would definatelly recommend to replace wiring and the airbag with your original one.
Removing the airbag may seem to be difficult but believe me it is possible! I have retrofited my seats too

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To gain acces to the side airbag a rear panel has to be removed and a part of upper upholstery detached. I have manual how to do it so let me know - I can share.
cheers