I feel that Buddha reached enlightenment by using wu-wei after giving up all efforts, just as Laozi suggests to do it, do you think my guess is right?
I think I agree with you. I won't go into the details of buddhas enlightenment because I am not a hinyana practioner, don't want to explain concepts that may contradict (without me knowing if they do or not). Though the late effort of buudha was pretty much "I will sit under this tree and chill until freedom or death" this is wu-wei, as in the essential meaning of it, effortless action. Buddha had already made the decision to obtain freedom, but it is as if the attempts were that which were blocking him from obtaining it.
Of course this is speculation as into the historical buddhas mind, and of course I again have possible differing opinions from my understanding that originally most likely did not come from traditional pali sources.
I consider myself to be a taoist, I myself have experienced fruits of meditation only when stopping trying to obtain fruits and just following my nature.