Forgot to say that you will still be exhausted whther you are breast feeding or not. You might find if you get too worked up over this issue , you will give yourself a lot more stress and feel even more tired. If your baby is not taking enough from you, cut back the solids a bit.
I would suggest introducing the cup, and as your baby drinks more from it, scale down your feeds. Introduce it inbetween meals so that it is not a battle with a hungry baby. HTH.