You might be able to do it through
ccsm. In the animations plugin, you can add specific rules for specific programs or classes of programs:
Clicking on "New" will bring up this dialog:
If you click on the
+ sign to the right of "Window Match" you will (finally) get to this window:
If you now click on "Grab" and then click on the menu you are referring to, the "Value" field will be populated with the ID of that menu and you can then apply specific animation settings to it. You may have to apply them to chromium as a whole if the drop-down list is not clickable but this should help you get started at least.