But do you really need to have the selected entry under the mouse cursor?
Once you have the right one selected with keyboard, you can just press Enter or Tab to validate the selection.

I often don't use the mouse at all, going throw the fields with Tab, then type the first characters of the country, sometimes press one or two times the "down" arrow for countries where many have the first same letter, then Tab for the next field.
I use only Firefox.