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What's perfect in this context? It's maybe a little counterintuitive because I'd think a perfect mechanical shuffle would be perfectly deterministic (assuming no mechanical failure of the device) so that it would be repeatable. Like, you would give it a seed number (about 67 digits evidently) and the mechanism would perform a series of interleaves completely determined by the seed. Then if you wanted a random order you would give the machine a true random seed (from your wall of lava lamps or whatever) and you'd get a deck with an order that is very likely to never have been seen before. And if you wanted to play a game with that particular deck order again you'd just put the same seed into the machine.
Perfect is the sense that you have perfect randomness. Like the Fisher-Yates shuffle.
In order to have a machine that can "pick" any possible shuffle by index (that's all a seed really is, a partial index into the space of random numbers), you'd need a seed 223 bits long.
But you wouldn't want perfect mechanical shuffles though because 8 perfect riffles will loop the deck back to it's original order! The minor inaccuracies are what makes actual shuffling work.
I'd probably have the machine do it all electronically and then sort the physical deck to match, not sure you could control the entropy in a reliable way with actual paper cards otherwise.