K.U.
I agree that if you are ready to get rid of the bottles, the best way is to get rid of them all, but I would add this: put all the bottles in a low cabinet and show the children, then show them all going into a bag to be gotten rid of. I would then let them "help" toss all the new sippy cups into the same cabinet and give them the choice to pick their own when it is time to get a drink. It will give them a little control in a big change. Good luck!
K.