Here's my untested idea that may work with easily found items you might already have.
Use two mesh net carrier bags for soccer/volleyball/basketballs. Place the ball in net and thread the handles of the other empty bag through the aperture of the net bag containing the ball until the ball is snug (If this isn't clear an analogy that may help is interlacing your fingers while you're holding a ping pong ball). Adjust the threading position in the nets until the ball is centered and then tie off with cable ties or equivalent. Attach strapping to make long handles.
Failing this, I think a DIY tornado ball with two long ends will work fine.