Psychological Egoism as a Logical Conclusion - Jim and the Indians Example

Let's have a look at a more complex example. This one deals with Jim and the Indians and it is suggested by Bernard Williams in his ”Critique of Utilitarianism”.
So, the situation is the following: Jim has a choice to shoot one Indian and save the other nineteen, or not to shoot that Indian and this way to convict all twenty to death. The principle question we are wondering here is the following: can Jim choose what is not motivated by his own self-interest? I am sure he cannot. To get sure, we'll repeatedly answer the question, "Why?"
Let’s assume Jim chooses to shoot one Indian, saving this way the rest nineteen. Why did he decide so? He must be thinking that it was better for nineteen to survive than for twenty to die. Why did he choose that and not something else? Perhaps he did it because he appreciated life as it was. So, he decided to do this because he wanted to feel pleasure knowing that he acted according to his values. And how about the guilt (or just negative emotion, if in general) that he may feel for becoming the killer? Was it altruistic that he agreed to bear this burden of guilt just to save lives of nineteen people? Although, why should he agree to undertake such a burden, if not for the pleasure he gains ( in other words the self-satisfaction from acting to his values) is harder then the pain he would experience (the guilt for murdering someone)? Again, trying to guess what was Jim's motives, I cannot find how to explain his motives in other way than by the pleasure he gains and the pain he escapes.
Let suppose Jim cannot kill another human being, and thus chooses not to shoot that Indian. Why would he choose this? Perhaps because he is unable to bear the guilt he would probably feel murdering someone. And what should he do with the guilt of knowing that twenty human beings died just because he refused to take any action? It is clearly that his decision was based on valuing the pleasure of knowing he did not kill over valuing the pleasure he would have experienced at saving the nineteen human beings’ lives. Though, it doesn't really matter, what Jim chooses. At the end, the choice made is based on his personal resoluteness of which of the two actions possible will bring him more pleasure (which is going to be the less painful) I fail to give any other motive that could be attributed to Jim while making the decision that would not go down to this.
What should be noted is that the question here is no way, "Does Jim get some kind of pleasure from whatever he chooses?" but "Does Jim choose one of the paths possible first considering what kind of pleasure he would get and what pain he would escape?" I am sure the first variant is absolutely true because the second one is also true.