Actually, that's not the only(or even best) solution.

It's pointed out in a previous chapter that intimate knowledge of such spells disables the regular patronus. Which is Harry's only weapon at this point - that threat. He can't say "I can kill dementors" without making the threat because he'll become an obvious man behind the break-in. What will he do, threaten to destroy them? They'll just send his ass to jail. No, he needs some kind of threat to the wizengamot, which in this case would be to ruin their Patronus spell. However, that still won't work because D knows what Harry can do and can likely stop him before he fully explains the his theory, and if that he fails at that, it'll be a pretty simple task to kill/disable him and then Obliviate the various wizards present.