Option 1 means, "Please have a look," using the honorific equivalents of 見る and くれる. This does not fit the context.
Option 2 is the given answer, to which I have no objection. However, I feel that option 3 is also a viable choice, because 見せる means to show something. Saying 見せましょう seems to me like the 部長 is allowing the 部下 to show them the 書類. I think this can be thus translated into English: Let's have a look right away then!
If my understanding of this usage of the volitional form is correct, why is option 3 not correct?