Super cute. Not sure why you need to use satin bias tape. That will be very slippery & usually is reserved for blankets. I'm sure it will feel nice & smooth, but if it causes you too much aggravation, you could always make a basic cotton fabric binding that would be a lot easier to work with. I will say that for the satin bias tape, you probably want to get clips (either the metal ones or Wonder Clips) as the pins will often leave a permanent mark/mar in the satin fabric.
Your nieces & nephews will be very lucky come Christmas Day!