Yes, continue with water changes.
You said in the first post that the betta and his friends have been moved to a new tank. Is the new tank cycled - did you move the old tank's filter over, or cycle the new tank's filter before moving the fish?
If everything in the new tank is new, you need to do daily water changes regardless of the betta's tail. Without a test kit you cannot know what the water conditions are, so daily water changes are the way to go.