The most common and most likely answer to this crossword clue is the 6 letter word DODGES
I've seen this crossword clue in The Daily Telegraph
D
O
D
G
E
S
More clues leading to the result DODGES
Buddy explains!

The straight part
We know that "Avoids/cunning wheezes" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case avoids/cunning wheezes = dodges.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does DODGES mean?
DODGES verb- To avoid (something) by moving suddenly out of the way.
- To avoid; to sidestep.
- To go hither and thither.
- (videography) To decrease the exposure for certain areas of an image in order to make them darker (compare burn).
- To follow by dodging, or suddenly shifting from place to place.
- To trick somebody.