It's not Finnick they can track down, it's Daisy. So if he interrogates her and then leaves her somewhere quickly, they can pick Daisy up without encountering Finnick.

The bigger thing is that after talking to Daisy they'll know that the fae know the location of the trapped fae, so this would prompt higher security at the Innovation Centre. As far as I know Finnick doesn't have the ability to erase or alter memories. His best bet is not to capture and interrogate Daisy at all. If he used his illusory powers to pretend to be another witch, he could trick her into giving the information away without ever realising that she's being duped by an enemy. Then no one would know that anything was up.