That vid is funny as hell! 20 years playing with nitro motors & never once has the flywheel just popped off from light taps like the vid says.They make flywheel removal tools for a reason,never ever hit the fltwheel with anything & dont pry with a screwdriver either,buy or borrow the correct tool.
If your flywheel nut came loose then you might not need the tool but use a new cone if it has, even if its a crapper steele cone instead of a brass one. Since you say your new the cones are not all the same so make sure you got the right one.
Why did you take the cooling head off? Just to see if the cyl is damaged?