When testing for the mean, the degree of normality of the population(s) is usually not of concern.
That is because the distribution of sample averages becomes normal as the sample size increases. Fortunately, even for populations with distributions that are quite non-normal, this effect is sufficient at a relatively small sample size -- like n=4 or n=5.
If it is suspected that the two suppliers produce different standard deviations, the variances can be compared with an F test. If significantly different, (or if the SDs are of practical difference size-wise) a modified t-test can be used -- like the Fisher-Behrens test.
However, depending on the situation, if one supplier exceeds the other in variability, that can be as important as a difference in means.
Stan