I have never been a fan of the snap attachment on pom-poms for several reasons: They are fussy to sew on. The pom-poms should be interchangeable between hats, but the pom producers are not consistent with the snap size or even which side the male/female of the snap belongs. And, the pom-pom can be floppy since the snap is sewn on the outside of the hat.
So I decided to go with the ribbon tie-on method when developing my faux fur pom-pom line. You simply pull the ribbons through to the inside of the hat with a crochet hook or by threading the ribbons onto a tapestry needle. The ribbon is thick enough so if you tie a tight bow, it will not come undone.
We just recently added these optional wood pom-pom buttons to our notion collection. These buttons just add a little extra stability when you tie your pom onto your hat.