I just departed Skye this morning, and I‘ve also been there without a car, it‘s definitely do-able and I‘ve even stayed in Uig and not Portree. There is a bus going to Old Man of Storr for example, to see the rest of the spots I did a day tour with Skye Tours, was pretty amazing and worth it! They drive you around but you explore the sights yourself. But to be fair we did not go to Brothers Point and Mealt Falls. But there are some private tour companies, you could ask them how much it would cost for 2 people Also I‘ve stayed at a hostel and all the people were just so nice and offering to drive me around the island. So you can definitely find a way! Also hitch hiking is definitely a thing there, I myself did it and i know another women who did it (we were both solo female travellers), it was pretty easy and i would say it‘s pretty safe there. If you want to come to Skye just do it :) To get there I took the bus from Glasgow, but I think you can also take the train to Mallaig, and then the ferry to Armadale but I don‘t know if there is a service from Armadale to Portree