Despite being the hedgehog's iconic and staple villain of the Sonic franchise, he doesn't really physically appear as himself in the miniseries. At most, he only makes a cameo as a scary, glitchy, distorted memory from Mecha Sonic that merely talks him down with minimal lines. 

A Mike Pollock-esque voice portrayal is the preferred way to go, but feel free to do your own take of the character if you want.