I could see it working as something like this.
Upon switching to the sword, you don’t draw it immediately but you holster it for a few seconds on one’s hip (since swords don’t have sheath’s). If you decide to attack within the time period while the perk is active, you’ll perform a powerful single strike equivalent to the properties of a heavy attack but with half the distance that eager edge provides and afterwards transition into the normal moveset. If you don’t attack you go into the normal moveset.