Here is a very generic wiring diagram for a 110cc machine. Click on the thumbnail for a readable picture.
Use this as a basis for your wiring. This uses a 5 pin CDI (AC powered) which it seems your stator is set up for.
5 pin CDIs are cheap and plentiful, so you could go that method, or rewire for a DC powered CDI. It is your choice. I'll help either way.
The only difference is that DC CDIs make the high voltage DC required (several hundred volts) by adding a DC to DC converter power supply inside the CDI to do the job. [All CDIs require moderately high voltage DC to operate]. AC CDIs make this required moderately high DC voltage by simply rectifying a moderately high voltage AC winding from the stator.
Six of one, and a half dozen of the other. They're both the same in terms of performance and efficiency. Choose your poison...
DC (4 pin) CDIs don't have a kill switch input. If you remove power to the CDI via the ignition switch, and the existing wiring doesn't keep up the 12 volts via the regulator/rectifier, then the engine will die. But is the regulator keeps the power up then the ignition switch won't work in many cases - it depends on how the regulator output is wired - is it before the ignition switch or after?
Handle bar kill switches can be wired such that they short the trigger signal to ground at the CDI (on a DC powered 4 pin CDI) instead of shorting the missing kill switch input. That is a bit of work to do that. This is why I would lean towards the AC ignition power approach since it is more common.