No, it's a negotiation at that point. I'm not a lawyer, but I'm fairly certain that the difference lies in whether or not you make a demand. If you simply say "I'm going public with this info on X date" and leave it at that, it's not extortion. If the other party decides they want to pay you to not do that, it's on them and you can negotiate from there because they made the offer. If you say "I'm going public with this info on X date unless you pay me" it's extortion.
I'm not sure it works like that. You may get away with it, assuming the lawyer never reveals your intent, but this sounds a lot like the "security" extortion rackets of the mob:
"Hey thought you should know, my 'security' company is currently for hire for businesses around town. We heard through the underground grapevine that a lot of folks may lose some product in their bodegas next month. Anyway, nice to introduce you to my 'security' business -- have a great month!"
If you revealed that your true intent was blackmail, and that's what this is, to your lawyer or anyone else then I imagine the intent in combination with the act is enough to nail you.
