I've been playing UC3's single player (some chapters, not a complete run of the game yet, though I do plan on it) on Normal only using melee (well... there's some instances where you HAVE to shoot people on a second floor or third floor because they'll never come down or you can never get to them). And it's been both fun and challenging. Developing strats and routes is also quite fun, I have to admit.
I know not many people check this part of the forum (I might post this stuff elsewhere) but here's some sample videos of me practicing and the strats employed.
Chapters6/7 Melee Only: http://www.youtube.com/watch?v=1-iy7IJT3eA&feature
Feel free to comment etc. Normal difficulty + Melee only is doable.. you don't have to put it on Very Easy/Easy!