They didn't need Takagi at all
After they kill Takagi, Hans and Theo walk to the vault and Theo says it'll take thirty minutes to break the code. THIRTY minutes. Not really worth the effort for Hans to go through the crowd to find Takagi, take him up the elevator, stroll around chatting about models and then do the whole intimidation and killing thing. If Theo had gone straight to the vault when they arrived and started working, Takagi telling them the password might have saved him about 15 minutes.