There are more words but they are from Tolkien's earlier conceptional periods. Tolkien likely changed these words as he evolved the aesthetics and completeness of the languages. You may even find languages that Tolkien later rejected. Do not mix words from different time periods unless you are familiar with the phonetic developments.
qasa-
verb. to shake, flap, nod, rustle
pal-
verb. to shake
A verb attested in Qenya Word-lists of the 1920s in a last of rhymes in -alle, with a past for palle “shook” (PE16/143). It might be based on a later variant of the early root ᴱ√PAPA “✱tremble” (PE16/143).
Neo-Quenya: Helge Fauskanger use this as the verb for “to shake” in his NQNT (NQNT), but I prefer [ᴱQ.] quas- as a more distinctive verb for “shake”; see that entry for discussion.
Below: Tolkien's Late Period (1950–1973). These are from Tolkien's late conceptual period — his most settled forms of the languages. Prefer these over the earlier ones above when composing new text.
A verb appearing as ᴱQ. qasa- “shake, flap, nod, rustle” in the Qenya Lexicon of the 1910s under the early root ᴱ√QASA (QL/76). Tolkien gave it the past form qasse after which he marked “(intr.)”. This perhaps indicates there was a distinct transitive past (not given), or that the entire verb was intransitive.
Neo-Quenya: I retain ᴺQ. quas- “to shake, flap, nod” for purposes of Neo-Quenya, but assume it is based on a Neo-Root ᴺ√KWATH so that it retains the same modern form. Its classical form would be quaþ-. For “rustle” I would instead use [ᴱQ.] hyasta-.