To the best of my knowledge and understanding, the term wu3shu4 (武術) literally translates as "military art" or "martial art". As far as I am concerned, the other meanings of "wu-shu" posted here are irrelevant to the fighting arts, since they do
not directly relate to martial arts or military methods and tactics.
Furthermore, the "wu" used in these other examples, wu2 (无) and wu1 (巫) are completely different words, with completely different Chinese characters to identify them, whereas they are all spelled the same in the English language, i.e. wu. Also, each of these words are spoken with a different tone pronunciation in the Chinese language.
I take the third example of wu-shu (无术)or (无術) to mean "having no art", in the sense of starting from scratch prior to developing or creating
any art whatsoever. I don't take it to mean "no technique", as posted here, in the martial art context of having transcended dependence on specific techniques as a fighter.
Traditional Taoist references to that latter concept speak of a mental state that is "without thought" and with "no mind" engaged in the process, a concept found in Chan/Zen Buddhist spiritual thought as well. Thus, the martial techniques are programmed into the deeper subconscious mind, yet are automatically and spontaneously employed without any conscious awareness of their presence or any mindfulness of their manifestation. There is a marked difference between this idea and simply "no technique", IMO.
As such, I consider this topic to be "grasping for straws' in proposing that there is any direct or obvious connection among these three terms.
Just my opinion.
Doc