I'm interested in starting a small business, or even just a hobby,
where I want to create my own shampoo and hair care line.  I am aware
what kind of special ingredients, fragrances, coloring dyes I want to
include in my product line.  However, I don't want to necessarily deal
with the hassles of manufacturing the product on my own.  Are there any
chemical/beauty product manufacturers that will produce the product
for me, in small batch quantities, at a reasonable price?

Hi! I think you'll find all the information you need just by having
the term to use. They call it "private label". So I did a Google with:

"private label" shampoo

and here's the first hit: http://www.vermontsoap.com/custom/index.shtml

A reputable company that'll do custom work.
I was once looking into just handmade soaps and lotions, and had a lot
of links, so I'm sure you'll find many more. Some were very nice and
not terribly expensive, either.

Good luck!