Voldemort is not mistaken because he chose to say "there is no good or evil." Rather, he is mistaken in saying that there is only power. No, there is not. Such a statement directly implies that the only people truly capable of being good or evil are those who have power, such as Dumbledore, or Voldemort himself. This is not the case. To cite an in-universe example, Peter Pettigrew. He was small in stature, unskilled, lacking in confidence, not particularly powerful, and neither clever nor intelligent. In no way could Peter Pettigrew be described as powerful. In fact, he is the almost complete antithesis of power.
In no way could you describe Peter Pettigrew as being powerful. And yet neither could you say that he is not evil, either. Not all men are brave, no. He could, in time, be forgiven for betraying his friends when threatened with violence and death. It is still a sin, and he would rightfully bare the blame, but one sin alone does not make a man. However, Peter continued with this, knowing full well that it was wrong. He was under no delusions that what he was doing was right, or even morally ambiguous. At no point did he ever consider confessing his mistake, as Snape did. At no point did he ever try to redeem himself in a truly selfless manner, as the one time he did something that was actually good, it was due to a life-debt. Peter himself claimed that he did not turn back out of fear of what Voldemort would do to him, but we know for a fact that this is a lie, because even if Peter felt that Dumbledore would have been unable to protect him, there was a span of time over a decade in length where Voldemort was not in the picture at all. At any point in time, Peter could have shed his disguise and come forward, freeing an innocent man from Azkaban and possibly even recieving leniency in his own sentencing. But he chose not to. Knowing full well that he had committed wrong, knowing full well that Voldemort was 'dead,' Peter still chose to continue forwards.
Voldemort's philosophy is disproven by the very servant he relied upon to resurrect him. If power was the only true determining factor, then Peter should have been worthless to all in all ways, and yet he was not. It was Peter, and Peter alone, who led to the downfall of the Potters. Often in fanfiction, Severus bares the brunt of the blame, but let us not forget that even with the partial prophecy, Voldemort could not have even found the Potters to attack them without Peter's information. Snape played second-fiddle at best to the death of Lily and James, which is ironic, seeing how Snape is far more powerful than Peter. And again, the idea is defied, as it was Peter who was instrumental in Voldemort's return. That is twice that Peter held the fates of many in the plam of his hand, twice that the destiny of the magical world hinged upon him. And yet he was not powerful.
A better choice of words for Voldemort might perhaps have been "there is no good or evil, only choice, and the context in which it exists." But then again, Voldemort is not a moral relativist at all, so claiming inaccuracy in his ideas in that context is a faulty accusation to begin with. Voldemort is a self-centric egotist. He judges the entire world based on a criteria that he himself excells at. Voldemort claiming that all that matters is power is effectively no different than Tom claiming that all that matters is your skill at barkeeping.
To judge the entire world based on a criteria deliberately weighted to place you in the top? That is not moral relativism. If anything, Cornathum, you have fallen into the very trap you decry. You chose to focus on the part of the statement that mattered the least, which is that "there is no such thing as good or evil." You immediately interpreted that as being morally relativistic, merely on the merit that it claims an absence of good and evil. Upon closer examination, we can clearly see that Voldemort's morality is not relative at all. It is very clear and quite concrete. All that matters is power. Period. It does not get any less relative than that. Circumstance does not matter. Perspective does not matter. Power is a concrete, demonstratable thing, and whoever has more of it is better than everyone else.
A superior example of fictional moral relativism might be the Joker, who claims that things like good, evil, justice, and crime are all meaningless labels that people give their perceptions of reality, and that the only true constant is the degree in which the individual deludes themselves as to the true nature of both themselves and the universe. To the Joker, everything is ultimately pointless, from Batman's efforts to fight crime, to the obsessions of his fellow criminals, to even his own actions. The Joker is a moral relativist.
If the Joker conversed with Voldemort, the Joker would probably point out that power itself is yet another meaningless label that Voldemort is applying to his own view of the universe, because a weak person could quite easily kill a strong one. The odds are just less likely of it. Ergo, power is pointless as well, because it ultimately means nothing in the long run. Voldemort would naturally disagree, and argue that his power is so great that it prevents him from dying. The Joker would then probably laugh, and say "but it doesn't prevent you from screaming just like everyone else." Then the Joker would set Voldemort on fire, or make a pencil disappear, or something.
After all, to the Joker, everybody is just an animal deluding themselves as to how things really are. Being a particularly strong or deadly animal doesn't make you any less an animal. If one of the pigs out of the herd can get stuck with a knife and not die, that doesn't mean it suddenly isn't a pig. It still squeals like a stuck pig, and it still bleeds like a stuck pig. It's just a pig that doesn't die when you stick it.