|I don't think you are going to be able to do it with a standard drop down.|
As I'm sure you know, the cell that is changing is dependent on the cell that contains the choice from the drop down. Simply scrolling or tapping through the list doesn't place the value in the drop down cell, so the dependent cell won't change.
There may be other methods as well, but nothing comes to mind right now.
You could do it with a list of values in a range of cells by using a Selection_Change macro, but not with a standard drop down.