I love climbing with camelback. Mine is fairly small, keeping it light, and usually that's enough for any given climb. Every time I pause to catch my breath or think about my next step, I take a few sips, instead of guzzling too much at once and then going without too long.
For another cleaning idea, stores that sell and rent band instruments and / or sheet music will usually have a "snake" (for a few bucks). It's a flexible shaft about 3 feet long that has a brush on either end, designed to clean out the inside of a trumpet, for example. It should run through the tube easily with no danger of losing your cotton fabric in there.
Oh, and +1 get an extra bite valve. Mine has come off a few times from getting snagged on a branch. I usually find it again, but a backup is nice to have.