Don't know if it's the same in India, but if you're doing it privately in the UK based on no revenue earning of any sort, the only rules would be laid down by the senders and receivers of the organs who would need to ensure that the organs get to the recipient safely and in the shortest time as some organs have a time limit on their use.
Factors to take into consideration would be things like is the destination going to be open when you arrive and is it an airport which accepts your type of aircraft; does the pilot have the necessary qualification to make an instrument approach if necessary.
A company at Fairoaks does this type of operation commercially and uses a Kingair, often operating between midnight and 6am, but there are other companies in the UK which use single engined aircraft.