If you bring up the Machine Control Panel (Ctrl-P or Command-P on a Mac), you can select the Extruder axis. In particular for the extruder, I would suggest using the "Custom Jog" button to move a specified distance. For example select Extruder axis and enter 225mm/min for the speed. Then enter 20mm in the custom jog box and press the button to extrude 20mm of plastic. You could enter -20mm for retraction.
If you're sticking with the "select axis then move" concept, perhaps you could add shortcuts like hitting x, y, z and e to choose the axis, and add a plus and minus button for the custom distance?