Influenced, you say, by “Not manmade material” (5)
I believe the answer is:
suede
'material' is the definition.
(I've seen this before)
'influenced you say' is the wordplay.
'influenced' becomes 'swayed' (swaying is a kind of influencing).
'you say' shows a homophone (sound like).
'swayed' is a homophone of 'SUEDE'.
'by not manmade' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for suede that I've seen before include "Soft leather with one side napped" , "Type of leather" , "unprepared material" , "Form of leather" , "leather material" .)