That should work. If you unpopper them at the top, take off the pad thingys then put the footmuff in place. Thread the straps starting with the shoulder bit throught the side slits first, then through the pad things then through the shoulder slits. You'll have to shove them a bit but you can get them attached back on with the pad things in place. With the strap between the legs, take off the pad thingy, thread through then put pad thingy back on.
Does that make sense?