Aunt Lydia crochet thread comes in colors--have you seen these? I bought a denim shade--I think they had two different types of denim, both dark and light, and I'm quite sure they had navy and black as well.
As long as you've got 100% cotton thread, you should be able to dye it. I guess you'd have to measure your proportions if mixing blue and black and test it on small sample pieces of thread as you add one color or another plus time it to get the right shade. You've got to let the thread dry, though, because it'll lighten up as it dries.
If you find a color you like, I think I'd try to unwind the entire ball, keeping it neat (good luck with that!) and put it in the dye vat. If you try to stick the ball in (cardboard and all), the color probably won't take evenly.
I know many knitters dye with Kool-Aid. It's supposed to be pretty simple and fun. You can google this and probably come up with complete instructions (sorry, I don't have time to do the search for you right now).
Another thought is that you could check out the home decor/trim sections of local or online fabric stores and see if you can find some lovely cording and tassels that match. Then you'd just have to sew them in somehow or add grommets and slip the cord through.
HTH,
Amy