Nice choice of sabers! I'll help you out.
First here are some pictures.
I'll be back to explain them in a minute.
So first thing in the first picture. When the switch is installed, the led needs enough room to fit in the body completely below the threads. The switch and the emitter hold the led in place.
Picture 2. Notice the flange on the led housing. That is the correct type to use. You can still use the one you have, but there is a catch. That flange seats the led when the emitter is in place. The type you have will bounce up and down. I know from personal experience. So you will need to add something to stop that. I use a piece of blue foam. The led housing you have will also fit inside some emitters, such as the war glaive. You got luck with your pick of emitter! It will allow some room for error on the switch placement.
Picture 3 is a buckpack. It regulates current flow. You don't really need one for a regular stunt set up like you plan for your son. On your saber, with one battery pack running two leds and an illuminated switch, you will NEED a buckpack. Also I use "JTS" connectors. They make trouble shooting and installs a lot easier!
Now picture 4 and most of your questions.
Stunt sabers use 4 AAA batteries. That is what you should use for your son's two sabers. AAA batteries in a 4 battery pack. Black wire goes straight to the led (or JTS connector). Red wire goes from battery to switch, then other side of switch to led. Very simple even if you use JTS connectors.
Your saber, running two leds and an illuminated switch, you will want more power than AAA batteries provided. So 14500 batteries that most sound sabers use. They look like AA batteries but put out a lot more juice. So use a buckpack too! The wiring for your set up is going to be a little different. I'm not to sure I can or even should attempt to help you with that one!
Some one else on the forum will come along and help you. I'm sure of that!
Keep us posted on your progress.