I found these instructions in a book I have for making fleece shawls. Cut polar fleece 22" x 72" (if you only have one yard of fleece, cut two 22" strips and sew end to end to make it 72"). You could make "cuffs" - cut 7" x 9" (or smaller depending on the size of the wrists) - sewed to the inside in the front corners of the shawl sewing down the two 9" edges. Slide your arms through the cuffs and the shawl wouldn't be sliding off.
You could make ties to hold the shawl together or add a button and loop. I don't think I would use Velcro - the fleece would be sticking to it all the time. Any thing that would hold the shawl closed and keep it from falling off.
You could edge finish the shawl any way you want - for our Linus blankets we do many of them using a wavy rotary blade. Quick and looks nice.
I like the idea of just 22" wide - you wouldn't have fleece bunched up behind your back when sitting.
Donna in Idaho