As far as I understand M-W test does not require normal distribution. Why do we need to test for normal distribution in this case? Some parameters as antibodies values, PFU counts and such are hardly ever normally distributed.
As stated, normality is not necessary for this test. However, the MW rests on the weaker assumption that the median is a useful way to characterize the data. So examining, in some way, that each group has a similar structure (e.g. unimodal, or if multi-modal having a meaningful median, etc...). In situations where you have interval data the SW test can therefore help assure you that the distributions can be compared in a meaningful way; provided that one recognizes that a significant non-normal result doesn't mean that the MW test is necessarily inappropriate - only that you would need a more careful consideration of the distributions at that point.