Doesn't the net catch the balls, meaning they don't hit the hard wood and you could use real balls?
I use BirdieBalls as practice balls, but those are decidedly for full swings outdoors, not chipping. I came to those cause I've never like any of the other practice balls actually shaped like regular balls, and I imagine it would be hard to dial in the light touch and distance control with short little pitches and chips with the whiffle balls.
Are you just worried about bouncing the balls off the hard wood when you miss the net? Maybe just consider it extra motivation to get accurate fast?! :-P