Hmmm. Well...it would work, yes. You COULD do it that way. But...why? What a lot of work.
Try this instead:
click pictureDoes it work? You bet. Did it hold up? See for yourself. Here are the same mittens after two Wisconsin winters' worth of wear by a boy, now in second grade, who wears these mittens (and no others) through every snowball fight and sledding adventure, every day at recess, after school and every other time he goes outside--and here, we've still got a foot on the ground (although thankfully, it is melting fast). These mittens are getting too small for him now, the bright colors have yellowed and faded, but he's still wearing them.
click pictureBottom line: for ribbing on felted garments, put away that waste cotton & bring on the superwash wool.
PS: Make sure to use a non-fuzzy yarn for the shrinky-parts, or the fuzz will get into the non-shrinking cuffs and make a mess. For further information about this, go to LIVNLETLRN, an illustrated entry on her blog.
PPS: If you want to make these mittens, a pattern is available for sale ($3.25)
You can go to the pattern store on Ravelry
You can go to the pattern page on Ravelry or
(you have been reading TECHknitting on: Felted Mittens with Unfelted Cuffs)