What can I do? Normality and Repeated measures ANOVA

I am conducting a Repeated measure ANOVA between and within-subjects (2*3*2*2). My dependent variables are response times and I am working with the mean. I have two samples with 22 and 68 participants. I tested the assumption of normality for the residuals, according to the S-W test, some of those residuals were non-normal. I have been reading about this but I am not sure if I need to conduct a non-parametric analysis or if the ANOVA is robust enough to be sensitive to that violation.

I would really appreciate some help.