Seems kind of circular. There isn’t a defendant until a crime is charged, and it’s assumed that there’s a crime unless a defendant says why it’s not a crime...
If “defendant” just means the person who is suspected, then Zimmerman already DID assert self-defense, to the police. This would only be an unlawful death if that assertion can be disproven. At least if a person is innocent until proven guilty.
There’s a sequence involved: a charge is made, that charge is that the individual unlawfully took someone’s life, the case goes to trial, at that point the defendant claims it was self defense, and the jury decides whether the claim that he unlawfully took someone’s life is true or whether they accept his excuse.
There’s nothing to keep the defendant from claiming it was self defense to the police, but that has no impact if the prosecutor decides to lodge a charge.
I think your route’s circular because a case where the defendant claimed self defense wouldn’t be a crime under your construct. How would false claims of self defense be adjudicated if just saying it was self defense makes it a non-crime?