Altering The Ten Essentials?
I don't know if it's so much as adding or removing as much as being flexible depending on your adventure.
I do a lot of dayhikes on the trails around my house that average anywhere from 1-5 miles, but are never more than 1/2 a mile from a neighborhood or street, and the trails are highly used. I will typically bring extra water and snacks, but will not bring all the 10 essentials.
If I'm traveling and going on a day hike to an unknown location, I will bring most, if not all, minus the tent or shelter, although when traveling for business, it's often hard to bring a knife or matches due to travel restrictions.
On any overnight, I bring all of them.
Regarding the map and compass, it's great to have them, but if you don't know how to use them, they are useless. Bone up on your map and compass skills at Backpacker.com's skills site. Additionally, having only a map or a compass does you little good. I guess if you are going to only have one, the map would be the one to have. You can use the sun to gauge direction as well as other options such as celestial navigation, but a compass makes it much easier and isn't dependent on weather.
Regarding repair kits, duct tape can fix almost anything including cuts, blisters, shoes that become flip-flops, broken tent poles, even holes in your sleeping pad. If you use trekking poles, you can easily wrap some around the pole, or if you use a water bottle, wrap some around it. You will have it when you need it and it weighs nothing.
In addition to Sunscreen and Sunglasses, I would also include a hat and lip balm.
One that I would add, I almost always carry about 50 feet of lightweight rope/cord www.rei.com/product/767607/new-england-3mm-utility-cord-package-of-50-ft tucked inside a small mesh bag with a couple of carabiners. I've had to use it for a variety of things such as lowering packs down when it was too precarious to downclimb with them on, stringing up wet clothes to dry them out, and hanging food / gear to keep the varmints out. The small mesh bag is great fro putting a rock in to heave it over a tree branch and keeps the rope and biners nicely organized. I've also used the rope as a tow when my hiking partners weren't keeping up. The rope can also be used as shoelaces in a pinch. I can find lots of uses for it.
Finally, on any long day hikes or overnights, I always pack my water filtration system. I use the Katadyn Hiker Pro.