Several problems with this whole thing. First, if you didn't do anything wrong, why lie? Second, you are ASSUMING that there are no other witnesses or video surveillance? Not a good idea.
Third, it would be his word against yours which means that there wouldn't be much of a case against you. Believing that you would be filed on in this situation, based on one dirt bags word is, in my opinion unrealistic. We can hardly get the Prosecutors here to file on people who we have evidence against, plus a written confession. Short of a written confession on your part, agreeing with the bad guy that you were the aggressor,I don't see you being charged with this, much less convicted.
Lying is never a good idea. Because if you said, no it wasn't me, and then the police ask to see your handgun that the dirt bag described, your caught in a lie. Now your credibility in this case is zero and the cops/prosecutor/jury are all going to believe that you were trying to cover up for something that you did wrong.
I realize that this scenario is based on a real story, but just like Holly Wood, the real story is, in my opinion never told, as it actually happened.
I don't want to be to critical here, but this doesn't take years of police experience to see the right answer on this one. At the very least, not answering any questions, or worse yet lying to the cops would ruin your reputation with the Police Department, if it was a small enough community. Then if you ever had to use force in the future, your name is already mud.