My son insists on carrying a stick around?

my 10 months old son picked up a small tree limb off the ground and played with it for a really long time. (with close supervision) after we took it away he cried wanting it back and now he wants a stick all the time. i was afraid to let him play with it while he wasn't being so closely watched(like while he was in his play pen) so i gave him an unused fly swatter to play with instead and this seemed to satisfy him but it looks weird when we go out in public (he's really attached.) does anyone have a safe alternative idea to give him?