Backing nine fair isle squares to cover loose strands of yarn

[lmc]

I am making Kristin Nicholas' design of a fair isle heart blanket for baby.
I think it is important to cover the backs of the 9 heart squares so the baby does not pull on the loose strands of yarn on the back of the blanket.
I am thinking of sewing cotton backing (fabric) to each square and leaving one row of stitches open to be able to attach each square to the other (s)...
Does this sound like a doable solution to you? Or do you have any other suggestions?
Thanks.
Lynn