The term wushu originally meant military art and is made up up two parts. One part is the character for ge (halbred) and the other is to stop. (In oracle bone text this part and corresponding character was actually the verb to run.)
The ge is strictly a military weapon (never employed by civilians) and the character is found both in oracle bone inscriptions and bronzes. The combination of the two parts of ‘wu’ can be interpreted in several ways such as using the military to stop insurrection or using the military to stop invasion and so on. The verb to run also refers to the infantry.
Wu is definitely in the realm of the military and would not refer to civilians practicing martial arts nor would it refer to dance .There are other characters that would be used to represent these activities.
In Chinese ****phones are common so I wouldn't make to much of a deal about the similarity in sounds. There may be an anthropological connection (e.g. both movement that may have ritualistic looking actions) but different root meanings to the actual words.