Costigan would not go against Evandau's decision. He would definitely push for further information and then accept that he needs to talk to Eshai (or Banner), taking no action on his own.

Costigan would pursue incarceration for 1-2 weeks (whatever you/Evandau feel/s is appropriate). He would also insist on actually committing a crime, instead of simply being charged with it, so that his story is solid.

(As an aside, I'm totally fine oocly if Evandau wants to make an announcement to that end or anything. Icly, Costigan would prefer less people know, obviously, but I'm good with whatever would be IC for you.)