FWIW - The registering isn’t so much a reprogramming as informing the car there’s a new battery in place. It changes the charging algorithm to match the battery’s needs. In theory if you don’t let the car know there’s a new battery you stand to shorten the life of said battery.
I’d google your model and see if it’s needed. (It is on most modern cars). Then poke around and see if there is an independent shop nearby that could take care of you. (Our shop is no where near $150 to register a battery).
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