A propriety choke most likely wont be designed to emit a magnetic field, if anything emision would be seen as parasitic so it makes sense designers/users would want this to be a minimum , it really depends on the inductor and of course theres bound to be some emission, just most likely not as good as a coil meant to do that.
Looking at your layout I'd say from the size your coils indeed will not have that great a coupling, if you look at my project, the coils are air cored and wound over 3 fingers, the physical size gives better coupling over a distance (10mm), but its still naff most of the energy is wasted.
Your boards are not necessarily scrap, you could just unsolder the chokes and place a coil around the outside of the board, your circuit will most likely work perfectly electrically, the chokes on the board are very unlikely to intefere with the likes of a 555.
If you look at circuits designed to charge phones and the like you'll see the coils are much bigger than a pcb choke, in the region of 4".