If you are flying SQ (Singapore Airlines) you can request at the check in counter for wheelchair assistance. This means someone will bring a wheelchair to the counter where you check in and wheel you through immigration, to the departure gate and all the way to the aerobridge (by the aircraft door).
The crutches should be allowed, but if they are not allowed, the staff will only take them from you at the aircraft door, put it into a special hold for other needful items such as strollers/wheelchairs. Such items will be brought to you once you disembark from the flight on arrival. Or, if you can't walk to your seat without them, they will be happy to let you use them all the way to your seat, then take them for check-in by aircraft side in the special hold. Alternatively, at check in, ask if they will allow you to keep the crutches. If it's not allowed, ask them for the special wheelchair that will bring you right up to your seat
On arrival, you will be met at the aircraft door with a wheelchair and an assistant to clear you through immigration and luggage. Your crutches will be returned to you right after you disembark (although it will be good to inform the staff that you have them in case they aren't aware).
This service is provided free. You do not need to rent your own wheelchair. SQ is pretty good with its special services, and especially if you are coming to Singapore, you can be sure you will be well taken care of
Ask if there's anything I haven't been clear on