I can think of several possible reasons why Clarke used Shadow Omegas in preference to the Hunter.
One is that he didn't know about it. Black Ops decided to keep it up their sleeves in case President Clarke got out of line.
Perhaps it was just a testbed for new technology which was subsequently expanded and used on the Omega. Or the Hunter was more difficult to build, Clarke needed an enhanced fleet quickly, so the Shadow Omegas were a compromise to get something into service while a fleet of Hunters was being built.
Another possibility is that Clarke knew exactly what he had, a stealthy super ship. This was not for use against external enemies. This was for use against Earth ships whose loyalty was questionable. Better to have the ship destroyed out in space and let others know that there were such rebels or risk unpleasant secrets being revealed. And if the ship's log showing the attack ever came to light, obviously that's an alien attacker, not one of ours - plausible deniability. The ship could be used for other dirty tricks for the same reason. By contrast the Shadow Omega was clearly a modified Earth design and could be used openly against publicly known enemies such as Sheridan.