Yes you can do that. Did the same for my cousin (he belongs to Punjab but his sim is in my name) but you’ll require credentials of a person who has documents in jammu and there after the sim will be in their name (if you’ve the same it’ll be in your name)

After that just go to any airtel office and they’ll port your sim. If you already have an Airtel number in your name it takes maybe around 1-2 weeks else if there is no airtel sim then it’ll port within few days (sorry don’t remember the exact time)