I doubt that you need a small base die, even if your rifle has minimum chamber dimensions. Once you fire the brass in your new chamber, it will reflect the dimensions of the new chamber and shouldn't require much more than slightly bumping back the shoulder when you resize it; essentially you're fire forming the brass to your chamber. If you have a match chamber, you might have to turn your necks in order to chamber the loaded round. Use a permanent marker to color the neck and shoulder of the case to see where the case sticks in your chamber. If the neck is what causes the difficult chambering, you have your answer.