If I get a charged creeper to the End, and kill the ender dragon with it, will a dragon head drop, or will I have to find an end ship?
From Minecraft Gamepedia:
Skeleton, wither skeleton, zombie, and creeper heads are also dropped by the respective mob if it dies due to a charged creeper's explosion. Player heads and dragon heads cannot be obtained as drops.
Hence, you can't use the charged creeper method. Dragon heads are only obtainable in an End city ship, so you have to go to an End city ship to get any Dragon heads.