why say "take" when we really mean "leave" (a piss, etc.)

Solution 1:

In the context of the sort of use that your question focuses on, the verb take functions as a so-called "light verb", "semantically weak verb" or "delexical verb". In other words, it is a kind of placeholder verb, a mere vehicle for transporting the semantically important content, namely pee, piss and so on.

As far as I can see, the kind of sense cited at point 7.a. in your list is the relevant one here.

Solution 2:

This idiom is general in that we can 'take action' or 'take an action'.

Most courts, however, have read the specific intent requirement to be satisfied in police excessive force cases if the defendant purposefully took an action which he or she knew or should have known violated the victim's constitutional rights. Police Violence: Understanding and Controlling Police Abuse of Force By William A. Geller, Hans Toch

For this usage, definition 7.a. To undertake, make, or perform: take a walk; take a decision is perfectly adequate.

take a wee -> perform a wee