Exposed Aggregate Concrete Walkway - replacement or pour over
My suggestion would be to blast away the surface dirt with a pressure washer, then clean it off with something strong like muriatic acid. (Or hire a neighborhood teen to do it. ;-> )  Then apply concrete bonding agent and leveling compound. Leveling compound is pricey, but it can be applied in thin sheets and it sets up fast (very, very fast).

You'll have to put some sort of forms up, but you can use cut up cardboard boxes, because you're only adding 1/8" (3 mm) or less to the thickness.

If you DIY this, please, please do an experiment with about 1 square foot of compound on some cardboard or something, first. It's really a mix-pour-spread-set product, so you want to be ready.