I'm not sure how tightly you have to relate your analysis to racism. Racism is a form of discrimination, and sexism is also a form of discrimination. The two do relate in that aspect. You could do an analysis of the naked woman in terms of sexism and sexual objectification. She exists in the story for two reasons. She is there to make the boys feel incredibly awkward, and she is there for the sexual titillation of the rich white men in charge of this horrible gathering. The naked woman exists as a sexual object to be ogled at by the men, and several of the men feel it is entirely appropriate to grope at her as if she were a mere object to be grabbed and passed around.
One angle I would consider in your analysis is how the woman is in a similar situation to the black boys. She is just as powerless as they are, because she is treated as an object. Grammar lessons tell us that subjects do the actions, and objects are the receivers of those actions. The woman is not in control of the situation, and neither are the boys. The real power and control rests with the people in the room that are rich, white, and male. The boys are male, but they are not rich or white. The woman is white, but she is not rich or male. Both the boys and the woman are kept from anything that might resemble the American Dream because they are not part of the one very specific group of people that the American Dream actually exists for.
The story “Battle Royal” by Ralph Ellison, although originally published as a stand-alone story, eventually evolved into the first chapter of Ellison's novel The Invisible Man. It is the story of the coming of age of an unnamed narrator, who is struggling to discover his own identity as a man, an adult, and an African-American.
As you write your essay on the symbolic role of the nude woman, you should consider the links between patriarchy and racial oppression. Both the nude woman and the black boys are figures oppressed by patriarchy, without power. They both serve as a form of spectacle, or objects of what Lacan terms "the gaze," a position which deprives them of agency and identity, constituting them as projections of the desires of the spectators.
In most coming-of-age stories, there is some form of sexual initiation. Here, however, the narrator does not have an opportunity to engage in some form of active sexual maturation. Rather than having a relationship to the woman, he, like the woman, is simply entertainment for the older white men.
As you work on your essay, you will want to think about how the stereotypical American Dream of the period in which Ellison was writing would include the young male protagonist succeeding in obtaining the blonde girl as a reward for overcoming obstacles in his life. Here, though, the disempowered African-American narrator is excluded from that system of blonde-white-female-as-reward, and himself, like the woman, is deprived of any independent identity or will, other than the ability to think subversively while his actions are constrained.