I believe that with the Control Toolbox (ActiveX) controls the dropdown arrows and other similiar features are designed to maintain a consistent look with other windows controls, which is why we are not give a property we can change to set the dropdown arrow width. As a result, I'm pretty sure that you have to change ALL dropdown arrow widths--which you can do from the Windows Display Properties dialog (right-click on the windows desktop, select Properties, select the Appearance tab, select "Scrollbar" in the Item dropdown, then set the Size property. Note that "arrows" include those at the ends of scrollbars, etc.
That did it! It also increased the size of the tabs, and that was also an un-requested wish I had. I wanted to do this after I observed someone working on a non-Excel program selecting from drop down lists and entering values from an pop-up on-screen number board using the mouse only. I was very impressed of the speed the operator worked with. The interface had really large drop downs and buttons and I realized the size does matter when you want speed and started to remarkably increase the size of my drop downs and buttons, but got stuck sizing the button in the combo box.