It looks like luck's highest perk is a dodge perk, which could synergy well with your agility build (since it also seems to have a dodge perk).
Luck also has grim reaper. Even though melee doesn't need vats as much as guns do, it can be very useful against run n' gun NPCs.
Better Criticals is hard to pass up if you are going for sneak attacks, especially if you put in the extra effort for melee sneak attacks.
Also, criticals could take the place of kill animations in Skyrim which can help to make the melee system feel more fluid.
As for the alternatives...
Strength is a good alternative, but it looks like luck has more powerful perks for a melee agility build (although S:9 and crafting could change things).
Also, Strength is often easy to buff in game and you only need 2 Strength for the melee perk or 4 w/ crafting.
Endurance looks fun as well, but if you are going to be really sneaky you probably don't need lots of Endurance.
One thing to consider with melee is many enemies do rad damage now, so you might want rad resistance with melee?