U can use ur own camera and take the photo. Get ur son to lie down on a white cloth and then snap the photo. Just edit the photo according to the dimensions specified in the website and submit online. I know iPhone has an app to take passport photo.
If you go to those shop, I believe they will get ur baby to sit on ur lap or u just hold his back.
I went to the ICA building to have baby's photo taken. They will let baby sit on a baby chair and distract him with a toy.
Very fast, less than 1min to take his photo. But before that, have to pacify him first and ensure that he is in a good mood