Why not just utilize the ContextMenu and ContextMenuItem classes that flash has to offer? I haven't found anything that necessitates me getting rid of the context menu, and Xeef is right it is against the MM license to do so.
About the solution in html, it's very involved, but you need to set the wmode of the swf to transparent ( I know it's odd ). You then need to create a div layer that sits over top of the SWF, this is where you are stealing the rightlcicks from the flash player, and you need to be sure to capture the right clicks with javascript and send them to the swf. This is possible, and it is compatible in both browsers. Good Luck

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_Michael