Those small led bulbs have a diode and current limiting resistor in them, they will run on AC fine. As for running a large LED type headlight though they will need DC. You can go the simple route, a four wire rectifier/regulator which is pretty cheap, and then run DC to the new headlights. The only problem is you will have the same issues you have with a regular headlight, it will be dim at idle, and will have a bit of a fast flicker to it without a battery to smooth the DC power out from the rectifier/regulator module.
What i would do, rewire for DC and add a small battery. You wouldn't need a lot as your not using it for electric start just the lighting. Its not hard to rewire these for DC i have done it a few times now, i will describe how you do it on a 200S, as you have it in a 200X frame it should be the same but i would have to look at the 200X diagram just to confirm that.
From the alternator you have a Yellow and Green wire, the green wire is the system ground, its grounded to the frame at the ignition coil mounting screw. The yellow and green wires are the two ends of the alternator coil down in the stator. If you buy a simple four wire rectifier/regulator what you need to do is take the yellow and green from the engine and connect them to the AC inputs of the rectifier/regulator. I can further diagram this if you decide to go this route and show you exactly where these wires go..
Then you take the yellow from the frame that used to plug into the alternator output and that goes to the DC output of the rectifier/regulator, and the green from the frame that used to go to the alternator now goes to the ground terminal on the rectifier/regulator.
Now you have DC on the Yellow wire up to your headlight switch and the lights will be on DC. The Black/Red wire from the ignition source coil in the stator is what powers your ignition system separately, don't touch that leave it be.
Now if you wanted to add a battery, the easiest way is a little 7ah gel cell battery tucked into the toolbox or strapped to the frame somewhere, you don't need a big 12-14ah battery unless you plan on running the lights a lot without the engine running. The 7ah gel cell is just there to keep the voltage consistent and the lights at full brightness at idle, it acts as a filter for the DC, a large capacitor can do it also but a battery is better in this case. To connect the battery you put the negative to the frame or to the green wire, as long as its grounded it can be either. The positive i run through a 10a fuse and tie that into the Yellow wire which is the DC output from the rectifier/regulator. The fuse just provides some safety in case the alternator coil ever shorts out, or a wire gets chaffed, etc. The engine will now run the lights and charge the battery and you can do just about anything for lighting options as long as you stay within the ability of the alternator.
The alternator will do about 4.5 amps, roughly 55w for the 200S. The stock headlight and tailight combo ran at 50w, 45w headlight and 5w taillight.
So HID is out of the question, too high of a turn on current, they generally take around 8-10 amps for initial firing and around 5-8 amps for running a mere 35w HID. I have played around with them a lot putting HID kits into offroad light housings for trucks and farm equipment, they work great but they are not energy efficient as say LED. I have a pair of 27w LED lights on my 200ES, from the sound of what you want for light these would be more like it for you. They draw 2a each, so 4a per pair, and you can still have enough power left over to run the taillight without draining the battery. Put an LED bulb in for the taillight and you will actually have some power to spare to keep the battery well topped off.
I run a 27w pencil beam and a 27w flood together as a pair, the pencil beam gives me the far out reach i want while the other flood beam gives me a lot of light right in front of me and to the sides.
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1984 Honda ATC200ES "Big Red"
1982 ATC200E "Hondie"
1988 TRX300FW "Project Quad" Still in progress....