What confuses me in your reply is that you've said, "The introduction of variation in nature is not guided," but also assert that "there are explanations." The lack of guidance would seem to suggest randomity, at least to me. But if a change, such as a particular mutation or new phenotype, has an explanation then randomity no longer applies.
I must agree with you that the term randomity can be problematic in these discussions. While its definition is straightforward, its statistical and philosophic implications are quite complex. Nonetheless, the term is abundent in the literature and frequently arises in these discussions, so it seems to me that it must be addressed.
Mutagens act without respect to fitness. Technically, they do not act randomly, because they can affect different parts of the genome in different ways. UV rays from the sun, for example, affect various parts of the body in different ways, depending on whether they are shaded or not. DNA is similarly shaded from harmful mutagens by structure and the cellular environment.