Evolution is not unguided or random. It is guided and determined by selection, which is what Darwin discovered.
The acceptance of evolution as a historical fact does not require a theory of how or why mutations occur. Darwin had no such theory. He did not even have elementary genetic theory. Change could come from any of a number of causes, but changes are nothing without selection, which is the shaping force.
If the evolutionary process is guided and determined by selection, as you state, then there is a clear implication that there is a guiding hand, rather than a blind watchmaker or no watchmaker at all. Guidance and determination imply an actor. If there are observable "laws" in nature that guide the evolutionary process, there is implied a lawgiver. Without guidance, one is left with random chance, the concept that, given a very large number of monkeys, chained to a very large number of computers, one of the monkeys will at some point type the Shakespearian play,
King Lear. The trouble is that, in view of the time limits imposed by the Big Bang theory, the odds against random chance eventuating in the universe and species that we know today are insuperable.
As for evolution being an "historical fact," by no means is it an "historical fact" on the order of Lee surrendering to Grant in 1865 or the fall of the Berlin Wall in 1989.