OK. We used jQuery to assign a handler function to the click event instead:

$( document ).ready(function() {
           $("#ButtonName").click(function () {DoButtonStuff();});
           $("input[type='text']").on("click", function () {$(this).select();});
});

To summarize:

There is already a switch in nopCommerce to make tinyMCE allow scripts, but it still doesn't allow the onclick attribute to be added to an input element (for HTML 5 compliance, I guess.) Since the jQuery code is in a script, it's allowed.

Thanks,
-Dale