How can I restore an iPhone without internet connection from my Mac when it needs and update to the phone?

I need to send my newer iPhone to the service and take back the old one for a while. I live up in the mountains and we do not have good connections here. That's why I always make backups to my Mac. Now, for some reason, it's not able to restore the old phone from the backup since it wants to update it first. I can't update since it's 3,4 Gt and it'd take forever in here. Not to mention how much it'd take the monthly capacity from the limited connections.

Both phones are iPhone 12 mini (since I love the small ones and unfortunately there is no alternative in the newer models)

It's been taking me hours today only to try to get the update, try to get all synchronised from another phone etc, nothing works. I need to be able to skip the update!

Is there a way to go around somehow?