Is it appropriate to use Mann-Whitney U test for each of four outcomes when outcomes are mutually exclusive?

I have an experiment in which we randomize primate subjects into high condition (n=9) and low condition (n=8) groups, and document each subject's behavioral response to 15 consecutive food exposure trials. Each subject's behavioral response during every trial is classified into one of four discrete categories (food A selection, food B selection, food rejection, non-response).

I am interested in comparing the frequency of each of these four behaviors among the high condition group to the frequency among the low condition group. Since the data are not normally distributed, my idea was to use a Mann-Whitney U test to compare the frequency of a given behavior in one condition to the frequency in other condition. I would thus be doing four tests, one for each behavior.

However, I realize that each of these four behavioral outcomes is not independent of the others (e.g., if food A is selected in a given trial, that means food B was not selected, etc.). Does this make using the Mann-Whitney U test and drawing conclusions from it inappropriate?

Someone suggested using Chi-squared by pooling all subjects and all observations, but I do not think that would be appropriate because I have 15 observations per subject, and it therefore violates the assumption that all observations are independent.