Replace the CDI unit by the coil, mine did the same thing, and its a pretty common problem. I did a dissection of the CDI box on here a while back. I found when mine wouldn't fire i could take the CDI unit off and smack the back side of it hard on the sidewalk a few times and then put it back in and it would fire right off.
The ignition switch being removed is not a problem, all it does is short the kill wire in the off position and turn on power to the light switch in the on position. So just leave it out for now and make sure the green and black wires that were to the switch are unplugged up in the headlight to rule them out. Also the kill switch on the handlebars goes bad sometimes, just take it apart and clean the contacts and get the dirt out, give it a little wd-40 and put it back together. You can unplug the black wire from the handlebar switch up in the headlight when it doesn't have spark, if it has spark then you have a bad kill switch.
But i still bet on the CDI. What year is it? My 84 i just removed the CDI and the round plug and put on a new square plug and a $8 CDI unit from eBay and away i went, been running flawless on that cheap unit.
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1984 Honda ATC200ES "Big Red"
1982 ATC200E "Hondie"
1988 TRX300FW "Project Quad" Still in progress....