From Brewer's:

"Shindy A row, a disturbance. To kick up a shindy, to make a row. (Gipsy, chinda, a quarrel.)"

I always took shindig to be a reference to clumsy dancing, especially Irish dancing, where you might get (or administer, in my case) an accidental dig in the shins. It's obviously an adaptation of shindy, but maybe my original thought is right as well.