What wattage are your carb heaters?
As resistance elements they will work on AC or DC. The simplest method is to hook them to your headlight wire and not use the headlight. That would have them operating only when the engine is running.
You can hook them up to the battery, but you need to add a switch. Estart bikes are good for about 70 watts peak and the worst you will do is run down the battery. If this happens you can kickstart the bike anyway, so it's no big deal to try it.
Those two wires on the stator are doing roughly the same job, the white wire is just farther up the winding for a bit higher voltage that the rectifier converts to DC. So basically some of the bike runs on AC and some runs on DC, but the total available power is still 70 watts.
I would add a switch and hook them up to DC. This gives you the option of warming the carb before startup when it is extremely cold (if needed).