I'm just a beginner sewing wise but yeah I think you could hand sew the seams if you haven't got a machine. Measure the size of the cushion you want to cover, length and width, and add maybe 10cm to each measurement for a seam allowance and to allow for the pillow stuffing. Although you have to have a way of finishing it off if you want the cover to be removable. I made some that closed with press studs for my ds's room. I. Sure there's a few really simple tutorials on the web. Just google "sewing cushion cover"
Just remember, measure twice, cut once!
Worst case scenario is you'll need to unpick it and start again