Choose the route of Pahalgam-Chandanwari-Sheshnag-Panchtari-Amarnath while trekking up to the cave. This is easy-approachable route, though it takes usually 3-4 days to cover this 46km journey. First 13km from Pahalgam to Canhandawari can be covered by a private vehicle operating there. But next (14+13+6) 33km will have to covered on foot. While coming down, take Baltal route, as it would save a good time for you.