When walking around the bima for hoshanos , it is preferable to hold the lulav in one hand and the esrog in the other, as that is the preferred way to fulfill the mitzva of the 4 minim, and thus one will be fulfilling the mitzva during the hoshanos. So balance the siddur somewhere; get one of those billfold-style hoshanos; be creative (write the hoshanos on a fellow’s shirt – back, and march behind him each day of Sukkos ); but keep the hands free for the lulav and esrog.
The Sukah has a special sanctity. According to many, this is derived from a passuk. Therefore, behavior inside a Sukah must be somewhat dignified.
Imagine how much more so inside your Shul!