I was in a tour group and Mt. Sinai was on the itinery. We were told the the climb up should take about 4 hours and the way down, about 2 hours. Since my spouse has had 4 operations on his knees over the last 20 years and I have had a severely sprained ankle a couple of years ago, I was somewhat anxious about our ability to do the trek. We also average 50 years. We could have opted out, but we didn't. We could have taken the camels, but we didn't. Why? Pure folly.
We made it in 7.5 hours, and thankfully, wasn't the last either in our group. But it was really at the limits of our endurance. But it can be done. First of all, we used knee and ankle guards with our sneakers. Even better if you go up in light trekking boots with excellent grip. Second, you need a walking stick of the correct length. Preferable if it is adjustable as I found I had to adjust mine to a longer length on the way down. Third, go at a pace that is comfortable for you. Trying to keep up with the Bedouin guide can give you a stitch. But at a slower pace, you might have have to start earlier so you can reach the top in time for sunrise. Fourth, as it is pitch dark, you need a torch. A headlamp would be best especially if you are using a walking stick as it frees up a hand. Fifth, dress warmly because it is 0C in December at the top, but in layers that you can peel off as it gets warm when you are climbing down. Bring gloves and a hat. I didn't find bringing my own half bottle of water useful as I could get drinks at the 7 stalls along the way. It only added to the weight in my backpack. Bring tissue as you will find your nose runny from the cold. Other things to beware: the 7km trail to the 750 steps is not even; it is very stony in several sections, which makes it easy to turn an ankle. Also, the Bedouins will come up on the side of the trail often without notice until their camels are almost upon you whereupon they will yell, "Camel!". My spouse got bumped by one. The 750 steps are, in some sections, just a pile of large stones, so you have to maneouver carefully. Close to the top, the wind can occasionally get gusty, and if you are 98 pounds like me, you can't help but fear being blown over the edge! Also, the wind can blow sand into your eyes.
If I were to do it again, I would take the camel up so I would have more energy to savor the experience of sunrise and the otherworldly landscape. I would do it leisurely on my own time, starting a little earlier to catch the sunrise, and coming down a little later taking many breaks of warm drinks in the huts. Having said that, many warm drinks may mean a trip to the toilet which is really a a hole in the ground with a bucket at the bottom, for which the Bedouin charges US$1.