StarEye: It has shooting (barely, better save those bullets!), and you do use the environment to get behind cover. If that's what makes it Uncharted, then just about every game involving shooting others people is Uncharted.
Talk about judging a book by its cover.
Even on hard difficulty the gun battles and ammo are plentiful. There are several sections where you can not use stealth to get by.
One part in particular was near the end where I snuck all the way though only killing a few enemies (out of dozens) and then being told that I can not continue because there are too many enemies in the area.