Welcome to your new addiction! Well, your basic parts list looks good.
I'll make a couple of suggestions based on experience, though: I'd stick to a 3.7V cell, as that's pretty much all you need these days, and make sure it's a regular one, not a high discharge (they're for Pixel blades.)
28 AWG wire is pretty much all you'll need for LED sabers. I'd suggest getting some multicoloured flat ribbon cable and stripping the individual strands out of that, rather than using just the one spool. That way you've got a colour coded indicator for what wire is going where and won't suffer any accidental shorts.
Finally, I'd suggest looking into some form of chassis to hold all your wiring and components together inside the hilt. That might be a little harder with a curved hilt like yours, but it's doable.
Good luck, and MTFBWY