I have tied many quilts. And have used many different items to tie with. For infant quilts I use Embroidery Floss. Fray the end before washing and make sure ties are made in such a way that they are secure.
I once made a crib quilt for my granddaughter. My daughter proceeded to attempt to take out the ties with no success. She thought the baby could pull them out and put them into her mouth.
I have used yarn, ribbon, cotton string, crochet thread (not happy with that too sharp, cuts fibres of fabric) and for fun, very short shoelaces. To use shoe laces, make two holes with an ice pick or something that will make enough of an indentation to let the tie of the lace go through. Happy tying!