This is an interesting and unusual question, assuming you mean, "What difference would the outcome of the story have if somebody other than Tessie Hutchinson ended up with the black spot?" Everyone participating in the lottery--something like three hundred people--stands a chance of getting stoned to death at the end. This would include children, even little Davie Hutchinson, who is only about two.
The author herself must have given a lot of thought to selecting the victim, since it was she and not the lottery that did the real selecting. Shirley Jackson must have decided that the victim should be a woman, since the story seems to allude to the incident recorded in the New Testament in which a woman was going to be stoned to death for adultery under the archaic law of Moses. The victim should be articulate and put up a lot of vocal resistance. Some victims--little Davie, for instance--might just stand there and get stoned to death by everyone, including Tessie and her husband, without a protest. His father Bill Hutchinson would undoubtedly be stoical and just let himself be bombarded until he fell to the ground. As your question seems to intimate, the outcome would not really be very different. Someone would die and the others would go on living for another year. This is what happens in real life anyway. Some people die and the others go on living.
It would be interesting to see how Old Man Warner would react if he drew the black spot. He is strongly in favor of preserving the good old traditional lottery, but he might have a sudden insight if he got the black spot. He might start telling the crowd it was time to abandon this old superstition and follow the example of some of the other more enlightened neighboring towns. In Old Man Warner's case, there would probably be only one round of drawings, because he probably lives alone and he and his household are one and the same. In fact, he might use that as a defense, saying everybody else got two chances and he got only one.
The outcome would be very important to the person who got the black spot, but it would have little significance for most of the other members of the community.