Azizi - In Cotswold Morris Dancing the use of sticks is more a case of various dances representing a fight. The sticks are more solid than the canes from the dancers you mention. If you watch some of the old Robin Hood films, you will see the fight where Robin meets little John and they fight with quarter staffs for control of a narrow bridge across the stream. Morris sticks are more based on the staff rather than a walking cane.
In some dances it is very obvious that "battle" is happening, in other dances it is more abstract.
Hope this helps you.
Quack!
Geoff.