Below is the WPIC (WA standard jury instruction) for assault (WPIC 35.50):
[An assault is an intentional [touching] [or] [striking] [or] [cutting] [or] [shooting]of another person[, with unlawful force,]that is harmful or offensive [regardless of whether any physical injury is done to the person]. [A [touching] [or] [striking] [or] [cutting] [or] [shooting]is offensive if the [touching] [or] [striking] [or]cutting] [or] [shooting]would offend an ordinary person who is not unduly sensitive.]]
[An assault is [also]an act[, with unlawful force,]done with intent to inflict bodily injury upon another, tending but failing to accomplish it and accompanied with the apparent present ability to inflict the bodily injury if not prevented. [It is not necessary that bodily injury be inflicted.]]
[An assault is [also]an act[, with unlawful force,]done with the intent to create in another apprehension and fear of bodily injury, and which in fact creates in another a reasonable apprehension and imminent fear of bodily injury even though the actor did not actually intend to inflict bodily injury.]
[An act is not an assault, if it is done with the consent of the person alleged to be assaulted.]
While an assault could be as simple as a "touching" of another (as that is clearly in the definition), using the above definition, prosecution UNDER THE FACTS YOU PRESENT is unlikely, as a tapping on the shoulder would not be typically "offensive to an ordinary person". The passage of a few days is no bar to one's being charged with an offense, but it certainly brings into question why an alleged victim didn't consider calling the police immediately upon the occurrence of an allegedly offensive contact.