My laptops battery requires a servicing/replacement.

My laptops battery requires a servicing. As per apple it will take the them 5 to 7 business days to replace the battery as they only do shipping to change the battery.

I have apple care but apple doesnt want to fulfill a replacement for free either because I have more than 1000 cycles on my battery(something I wasnt explained when I was buying apple pay). Is it even worth having apple pay?

Any ways, Is there a way for me to buy the battery separately or whatever parts being delivered to me and I replace it myself? Or any place to get the repair/replacement done within a day?