Don't tell me Shinichi is joyboy of this universe trying to defeat a fucked up organisation called men in black. And the men in black once made a prophecy 800 years ago which said that 800 years later a silver bullet with come and destroyed the organisation for good and I think I will stop.
It's already a suicide mission in the first place, hence the heart monitor. Conan is a consummate gambler, who only ever gambles with his own life. He's gambling the entire arc, ever since Vermouth makes it expressedly clear she knows who he is.
If the plan works, he and all those he knows of who (can/will) work to defeat the BO gains vital intel. If it doesn't, all those he knows of who (can/will) work to defeat the BO will still gain vital intel. He will just die or suffer a fate worse than death. And Conan is perfectly fine with that.