It's not as simple as that.
"Enemy combatants" come in two flavors: Legal and Illegal.
Consider the case of Herbert Hans Haupt, American citizen, captured in World War II in civilian dress, on U.S. soil planning to commit acts of war against the U.S.
In Ex parte Quirin, the U.S. Supreme Court ruled that Haupt was inded an "enemy combatant" and could therefore be tried before a military tribunal.
However, by not wearing a uniform and by not carrying arms openly, Haupt, like our al Qaeda friend, had violated the Rules of War and was not merely an "enemy combatant". He was an "illegal combatant".
Three days after the U.S. Supreme Court ruling, a U.S. military tribunasl found Haupt guilty of being an "illegal combatant". Five days after that, Herbert Hans Haupt, American citizen, enemy combatant and, most importanlty, illegal combatant was executed.
My only point is that if he denies he is an enemy combatant at all, and he is a U.S. citizen, he ought to get a hearing to determine if he is or not. If he found to be an enemy combatant, then he can be dealt with under the process you outline.