If one holds that Jews living outside of Israel should sit in a sukkah because of Sfeika Dyoma (We aren't sure what day it is), then why shouldn't we shake lulav and esrog? Worst comes to worst we are just shaking a bunch of leaves?
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Sitting in the sukkah can be considered a "passive" action, for without saying a berakhah (ברכה) all we're doing is simply sitting and eating outside. However, shaking the Lulav is an "active" or "positive" action which is very specific to Sukkot, and as such, it is not done for the same reasons we don't say a berakhah when sitting in the sukkah on Shmini Atzeres. (In other words, "Worst comes to worst we are not just shaking a bunch of leaves.")
In addition, the Talmud (Sukkah 46b) rules that the Lulav and Esrog are muktzah on Shmini Atzeres.
(Answer is loosely based on http://www.askmoses.com/en/article/103,21341/Do-we-eat-in-the-Sukkah-on-Shmini-Atzeret.html )
For more information on why we don't say a berakhah when sitting in the sukkah on Shmini Atzeres, please see: