I would trace around the Uke onto paper and then add 7cm all the way around: 2cm for a seam and some extra space because the shape will shrink a bit when you quilt it.
Cut two of these from your top fabric, bottom fabric and wadding (you will have 6 Ukulele shaped pieces of stuff in all).
Then cut strips as wide as the Uke plus 2cm on each side for seams (eg; if the Uke is 6cm wide, the strip should be 10cm) and as long as the circumference of the Ukulele shaped piece - you may need to sew a few pieces together.
For ease of sewing, I would quilt the front and back pieces as you like, but just sandwich the wadding for the strips without quilting.
After you have quilted the main pieces, check them against the size of the Ukulele and trim if need be (but don't forget to leave the seam allowance!).
Stitch the front and back to the sides, leaving an opening as required to get the instrument in and out again.
A zip will be the nicest finish, but you could also just finish the edges nicely and sew some ribbon on either side for a tie-close. I wouldn't choose velcro myself - always seems easy but hard to make look neat.