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Notice that you don't "click" a mouse. You point to an object with the mouse point and you press the mouse button. And the mouse button makes a clicking sound. Click is not an action, it is feedback. 

In other words, the current word is not a literal description of what you do. It is a word chosen arbitrarily to represent a complex action with multiple elements. 

But tell a naive computer user, someone who has never seen this class of interface before, to "Click OK" and they will be totally at a loss for what to do. 

But naive computer/phone/tablet users are not your audience. Those that are not two years old are outliers and will receive instruction from the experience users around them in the basic vocabulary of computer UIs. Your audience is people who know this stuff because they do it all day, every day. 

If you tell them to "Select OK" they are not going to sit there puzzling out how to highlight it. They know what an OK button is, and they know what to do with it. The verb here is actually completely a throwaway word. It doesn't matter what it is. There is only one thing you can do with an OK button, and just about every other UI element, and your users all know what it is. 

So the only way to get the verb wrong is to come up with some word so unusual that it makes the user question your sanity or thier experience. 

If you were to write "click" or "tap" or "push" or "touch" everyone would know what you meant. A few picky/snarky people might point out that the verb was wrong for their device, but not one of them would be confused as to what to do. 

But if you want to avoid that then "select" is indeed the correct term to use, because it is the common generic term for "activate this control from among the many available". The fact that it is a term for other forms of interaction with the UI is in no way confusing to anyone with experience using these UIs, which is virtually everyone. Like so many other terms that appear formally ambiguous, it is actually completely clear in context. (If you have to defend this to technies, point out that this is polymorphism at work. Each class of control is selected in its own way using the same command. The human brain does polymorphism very well.)

Other terms have been tried, but they all sound weird and unfamiliar. And sounding weird and unfamiliar is the one way you can get this really wrong, because when instructions sound weird or unfamiliar, users lose confidence either in themselves or in the instructions, and then they are apt to do the wrong thing where they would otherwise have done the right thing with no instruction at all.