Common anode, correct. You'll be wiring the accent LED in with the blade LED (L1, L2, and L3), so you need to match up the positive/negative. Can't wire a common cathode because then you'd be wiring negatives and positives to the same pads which won't work well for you at all. I believe you could do it the other way, but then you would have to switch everything else around as well.
There's no resistor on the green die for the cree because PRIZM has adjustable drive settings, and since the green cree die runs at a voltage that is very close to the forward voltage from a 3.7 V battery, even the smallest resistor TCSS offers will be way more than you need. A simple drop in drive settings will work in the place of a resistor in this case.
Note on resistors, by the way--they can get to be pretty freaking big and may not fit very nicely. I would suggest trying to source from someplace like mouser.com and look for things that aren't massive like the ones I got for a recent stunt build were.
Also notice that the dotted lines indicate a possible way to wire in a recharge port. While a removable cell would work with PRIZM and the board does have a deep sleep mode, it will always be drawing power from the battery. A recharge port is a good way to eliminate idle energy consumption and can be wired and placed into the chassis or in a hole in the hilt itself.
Thank you Erv for verifying the diagram. Apologies Modano for the late response.
Cheers!