Apparently, someone has tried this and it works! Scan your membership cards into an iPhone gallery and amazingly enough a barcode reader can scan them...
So instead of writing down the numbers I scanned in the cards -front and back side- and stored them as images on my iPhone.
To test it out I went to the local hardware store and asked the girl behind the counter if she could scan the barcode from my phone. The first look I got was pure amazement. To her the physical card was transformed into a picture on a shiny device. On top of that the barcode was scanned successfully. The result; a slightly confused girl and a happy me.