Similar questions do not deal with “somatic only” spells (they only say “no” due to lack of access to verbal or material components, see the link)
Wild Shape states:
You retain the benefit of any features from your class, race, or other source and can use them if the new form is physically capable of doing so.
Could a druid wild shaped into an ape still cast non-verbal & non-material (somatic only) spells, for example:
Thunderclap: [..] Components: S [..]
My logic: Ape has hands = can clap?