Slightly change start of walk through wood (5)
I believe the answer is:
tweak
'slightly change' is the definition.
(to tweak something is to make a small change to it)
'start of walk through wood' is the wordplay.
'start of' says to take the initial letters.
'through' is an insertion indicator (inserted letters go through the word).
'wood' becomes 'teak' (type of timber).
The initial letter of 'walk' is 'w'.
'w' placed into 'teak' is 'TWEAK'.
(Other definitions for tweak that I've seen before include "Nip" , "Slightly alter" , "Make minor adjustment" , "Edit" , "Adjust finely; pinch" .)