As a workaround you can add a very tiny radius to the sharp edge then apply your desired blend. In the attached model I used a .0001 blend on the sharp edge to approximate what you are after.
If the tiny radius is unacceptable, it can be removed using John Baker's suggestion in this thread:
Thanks for your quick reply. Everything seems to be great with those tips, besides the fact that after healing it becomes a 'body'. But I guess there's no other elegant option that can solve this.