Ah. Have you tried Gaffar Market in Karol Bagh? That is your best bet to be honest. If you cannot find it there, then it's a no go and your only option would be to approach the Apple Service Centre. Btw, have you tried asking for the price at the service center? They might have rejigged their prices for all we know.
I am not sure about importing batteries, you'll have to look into that.
In EU it costs around 110 EUR from Apple/authorized SCs. Will possibly cost you more than 10k in India, and ipad batteries are almost always OOS everywhere. iFixit guide and AliExpress are probably your best options.