We said that the reason why you can't shake the lulav and esrog on Shabbos is because you might carry it into the street. My question is that we learnt in Maseches Beitzah that Beis Shammai says you're not allowed to carry unless it's for Ochel Nefesh so according to him would you be allowed to shake Lulav and Esrog on Shabbos since if you say "V'ya'avirena Daled Amos Birshus Harabim" you should say it on Yom Tov. So according to Beis Shamai you'd be allowed to shake Lulav and Esrog on Shabbos!
Perhaps the Gezeirah was only on Shabbos which is Chamur because it is a Chiyuv Misah. Yom Tov is only a Lav.
Rav Yitzchak Isaac Chaver asks your question in Beitzah 12a. He answers that the Maskana of the Gemara in Sukah (end 43b) is that we only do not take the Lulav on Shabbos because some people do not know the Kevi'a d'Yarcha, and therefore have a Safek if they must take the Lulav, whereas it is certainly Shabbos and if someone is Ma'avir four Amos he will definitely be Over the Isur. However, as far as Yom Tov is concerned, if it really is Yom Tov, there will be a Kiyum of the Mitzvah, and if it is not Yom Tov, there will be no Isur at all.
Dov Freedman