Jason, if you haven't figured this out yet, you can change the data frame properties to a different projection. You will get a warning when you try to edit to let you know that the spatial reference doesn't match the data, the shape will of course distort, I would check the edit results carefully, but this will change the displayed coordinates in the edit box.
Below...features class is Alaska Albers....data frame set to NAD1983. Coordinates showing in decimal degrees.
Just changing the data frame units does not change the units in the edit sketch window for me. The only thing that will changes seems to be to set it to projection such as GCS_WGS_1984 that has angular units rather than linear units.
Units in the sketch properties window and the guide that shows up in the lower left when editing seem to be controlled only by the coordinate system and not the data frame units