I'm having a bit of trouble understanding your itinerary.

You want to go from LAX to DEL with stopover in MUC? Fine. But you do not want to go back from DEL to LAX but instead book a DEL-LAX ticket for a day before you actually arrive in DEL? Your office is only paying DEL to LAX? But you don't want to flt that leg... I'm confused.

Anyway, throwing away segments of a ticket by cancelling them can result in getting the ticket repriced and instead of getting a refund you will have to pay up e.g. from a round trip ticket to an one way.