I think the Aunt Minnie look everyone fears is possible if the fabric is too cute (unless that's the gift theme). If the fabric is opulent like this embroidered floral silk, I think your gift just got upgraded. Fabric gift wrap makes sense these days, it can be re-used, recycled, and regifted many, many times over. I can see this look twisting in many directions, Pucci, gorgeous chiffon, lots of possibilities. You can use pinking shears if the fabric is casual and fun, anything more elegant will need edges sewn. Watch for clear-out pricing on fabric remnants, especially raw silk as it has the stiffness needed for a good "pouf". Anything slinky is going to fall more than pouf, though not a bad idea either. You're going to feel positively "green" with your regift wrap. As soon as I confirm the sizes I will post again on this idea.
Little Side Tip: If you can't quite work fast enough to tie the ribbon while holding the pouf, then use an elastic band, then tie the ribbon bow. If careful, you can then go back under and carefully snip the elastic.
Both photos by Sande Chase - Oooh la la Cadeau