WebButton with menu without disclosure

Currently, if I place a WebButton on a page and add a menu to it, it will display as a button with the disclosure triangle attached to its right. Clicking on the disclosure shows the menu, clicking on the button does not.

I’d like to show the button itself, no disclosure, and have the menu show when clicking on the button.

What I have tried so far is a contextual menu instead of a standard menu. The button now looks fine but you have to right-click to show the contextual menu, and I have not found a way to show the contextual menu programatically when left-clicking on the button.