Make it so that when Alt+H dialog appears, the list of files is focused and the second item from top (i.e. target for Alt+G) is focused. Thus pressing Up/Down arrow keys changes selection in the list without the need to click inside the list with the mouse to focus it.
If the list has fewer entries than 2 (1 or 0) then do whatever is easier to implement (e.g. don't focus at all, or focus 1st item).