I personally don’t think you should miss Skye. I was determined not to miss it, despite not renting a car. 20 years ago when my son was 10, we back-packed for 3 weeks through Ireland and Scotland using public transport. We took the Scotrail sleeper from London, and arrived Kyle of Lochalsh the next morning. From the train station we boarded a bus which took us over the (then new) bridge to Skye. From Kyleakin, we took a Post Bus (small mail delivery vehicle mentioned in Ricks guidebook) through Broadford, and to a BnB (Coriusk House) in a southwest peninsula near Elgol (old name Elagol). There was nothing around except glorious hills, red deer in the fields every morning, sheep, highland cattle, and a long walk down to the stunning Elgol harbor. The BnB had only 3 rooms, and they also served dinner if you wanted it- fresh local scallops, And other local products, so knowing this in advance, we were not needing a vehicle. We walked/hiked every day, trying different routes, —-on day 1 a border collie befriended us and joined us on our rambles every morning after breakfast. From Elgol harbor, there was a boat tour (called Bella Jane) to an inland loch Scavaig, so we reserved this one day and walked a mile to the harbor, took the boat at around 10 am, along with others who had driven to Elgol for the same boat trip.
It was spectacular - there were seals everywhere, eagles, and the most beautiful clear blue water. After docking near the loch, We had to climb a bit to reach it, and it was more than I imagined, land-locked, deep, and stunning -
Yikes I’m rambling - what I’m saying is that these 5 days without a car were the best days of our entire trip. One more thing, on our last night, the BnB owners invited us to a Ceilidh, a friends birthday party, with trad music and lots of brew....an unexpected joy. So, you never know what will happen - no, we did not experience all of Skye, but we experienced the real Skye. Like life, it’s what you make of it.
PS -As of now, there are mini van tours of Skye starting from the town of Portree, going to most of the Natural and historical sites. If you stay in Portree you will have everything you need in walking distance and the opportunity to explore with a mini van tour or on the island bus, and maybe meet other travelers to hang with. Go for it.