Though highly controversial, police use show-up identifications in several situations

Though highly controversial, police use show-up identifications in several situations. Consider this scenario: You are called to a local drug store for a shoplifter that just ran out the door. The only thing you know about the suspect is that he is wearing blue jeans and a red shirt, and that he was headed toward the West. On your way to the drug store you see someone matching this description running west. You stop the person but are still unsure if he is the shoplifter.

Would a show-up identification be appropriate in this scenario to identify if the detained person is the suspect?