electro.bazaar,
In a brick and mortar shop, if a customers asks the shopkeeper to deliver an item to a particular place, then the shopkeeper may refuse it as it is a physical brick and mortar shop.
However, in an online business a seller can't give a reason to the buyer that they wouldn't ship the item because their shipping partner doesn't support the buyer's location.
Please bear in mind that the buyer is your customer and not your shipping agency. You need to replace your shipping agency and tie up with a competent and professional agency to ship your items.
And if your items are cheap, then prefer India Post Registered Airmail. It will reach even to the highest point in Ladakh to the dense forest in Assam...
Good Luck.