Staggering -- eschewing wife's maxim! (6)
I believe the answer is:
saying
'maxim' is the definition.
(I've seen this before)
'staggering eschewing wife's' is the wordplay.
'staggering' becomes 'swaying'.
'eschewing' is a deletion indicator.
'wife' becomes 'w'.
'swaying' with 'w' taken out is 'SAYING'.
(Other definitions for saying that I've seen before include "Saw" , "Speaking; adage" , "Speaking; twenty-two Ac" , "Expressing in words" , "Delivering" .)