Then he casts detect magic. He scans the bedroom and the pipes in the ceiling, just out of curiosity. Then he leaves the bedroom and scans the wizards' workbench.
"Someone open the door for me!"
Assuming someone will then open the door to the north of the workbench, Wiglaff will scan that room (which he's assuming is the mirror image of the whisper bedroom).
Hopefully all this can be done in a single turn (the spell lasts for two turns).
Here's is Wiglaff's path, in blue, and the areas he is scanning (in light green). (I think that's the right location for the wizard paraphenalia.)