I am sorry luckyagm, if your are a DJ at FM Studio Room then it's probably not your job to set up the broadcast equipment. I am pretty sure that a well settled Radio Station would already have an equipment (phone interfaces) for broadcasting the calls/conversations whether they are live or recorded earlier.
The delay is needed actually when airing the show on, if it's going live. "Delay in calls themselves" is senseless, there is no meaning of it. You talk to the callers live without any intentional delay, but actually the conversation you both have, is being broadcast with intentional delay to help editing/removing any kind of profanity.
BTW, to my knowledge, all the Radio Stations have these equipment which are already in practice. Or else they don't get licensed to broadcast live shows if they don't have required equipment.