The Talmud says (Sanhedrin 74a):
The ruling of the mishna is stated with regard to a young woman who was raped in a case where one was able to save her by injuring the pursuer in one of his limbs, so that it was not necessary to kill him in order to achieve her rescue, and it is in accordance with the opinion of Rabbi Yonatan ben Shaul. As it is taught in a baraita: Rabbi Yonatan ben Shaul says: If a pursuer was pursuing another to kill him, and one was able to save the pursued party without killing the pursuer, but instead by injuring him in one of his limbs, but he did not save him in this manner and rather chose to kill him, he is executed on his account as a murderer.
So even killing a certain perpetrator of a very serious crime (rape), who certainly committed the crime, when that killing was avoidable, makes one a murderer. Therefore in the context of the question here, where one kills someone who has not even committed the very serious crime (murder), and apparently does not wish to do (it appears they want a threat not to actually kill), to kill them when avoidable, is surely murder.
Since their action appears to be avoidable by handing over the wallet, shooting them instead would apparently be murder.
And again (same source):
From where do we derive this halakha with regard to a murderer himself, that one must allow himself to be killed rather than commit murder? The Gemara answers: It is based on logical reasoning that one life is not preferable to another, and therefore there is no need for a verse to teach this halakha. The Gemara relates an incident to demonstrate this: As when a certain person came before Rabba and said to him: The lord of my place, a local official, said to me: Go kill so-and-so, and if not I will kill you, what shall I do? Rabba said to him: It is preferable that he should kill you and you should not kill. Who is to say that your blood is redder than his, that your life is worth more than the one he wants you to kill? Perhaps that man’s blood is redder. This logical reasoning is the basis for the halakha that one may not save his own life by killing another.
So a person is not permitted to certainly save their own life (which will certainly be ended in an unlawful manner) by committing a killing themself. Therefore it is hard to see how a person could be permitted to only potentially save their own life (which is only maybe going to be ended in an unlawful manner) by committing a killing themself.