There may be several causes of knee pain when pushing a wheelchair, not all of which are related to the pushing activity.
The incapacitated patient sitting in the wheelchair may be overweight or obese, and the caretaker has less strength to push such a heavy weight around.
The knees of the caretaker who is pushing the wheelchair may have become arthritic, and the pushing aggravates the pain.
To help strengthen the knees, wear knee braces (available at any pharmacy) and try to push the wheelchair with the weight of the upper torso by leaning forward and pushing the wheelchair with the strength of the arms and hands instead of using the knees as pivot. When leaning forward and pushing with the arms, try keeping the knees and legs straight. Use the balls of the feet as pivot and point of pushing.