The peace officer has to qualify with the gun, so unless he's going to get himself a 4" barrel gun for that and another shorter barrel gun to carry - thats what he's dealing with.
If it were me I'd do some research and get the specs on back up gun (BUG) requirements from a number of agencies - I wouldnt be surprised if this might
be one of the few departments in the country with such a 4" barrel requirement. Bring the information to your agency administration so they can update the regs.
As for the gun itself - - - -I've heard that a number of agencies like the no lock S&W J frame. (Some have said, but I haven't researched it deeply, - - - that the no lock gun was produced to comply with police agency back up gun specifications).
On of the best places on the net to research info on back up guns from professionals is the Terminal Ballistics sub-forum found at M4carbine.net. Many military and police folks go there. It would be interesting to post your question with the 4" barrel requirement there & read the response: