Kam Snaps are my first thought...I have found them to be very secure and snaps have been used for decades on all types of baby products without any problems...but very old school would just be a tie on each side that could be tied into small bow...A lot depends upon how each feels about any baby closure...
I don't know anything about babies, but using elastic comes to my mind.
Kam snaps? But I would be concerned they could be chewed off. What about short length of ribbon or tape just long enough to tie but not long enough to choke.