But that's actually a different question. The OP asked whether any of the defendants offered as defence "We didn't do that". At most, as you say, they offered as defence "I didn't know about it". Most famously, of course, Kaltenbrunner, head of the RSHA after Heydrich's death, who claimed he only rubber stamped all those orders and didn't really look at them.
Again, it depends on who you're talking about. Since most discussions of trials will automatically default to the main Nuremberg trial, there is the problem that only 1 of the defendants was an active SS officer, Kaltenbrunner. The others all could rely on some attempt at plausible deniability, even though their complicity could be shown in other ways, to the extent that it was relevant. The military figures were not involved in a significant fashion.
The question should be: did SS officers serving in units involved in the Holocaust deny "it happened" when put on trial? The answer is some did, invariably without conviction or against better knowledge available from documents. Thus, in the 1960s, Karl Wolff resorted to flat denial of knowledge about the Final Solution even though he received letters about deportations to Treblinka and Belzec. This wasn't a convincing denial and the form of the denial is not a meaningful negation, because it was a Mandy Rice-Davies Defense ('He would say that, wouldn't he?') at best.
The best known case is Josef Kramer, commandant of Birkenau then Belsen, who denied there were gas chambers at Birkenau until, he said, he learned of Hitler's death, which released him, he said, from his oath of secrecy. So by his trial he was fully admitting things.
What is worth underscoring is how many SS disclaimed knowledge even when they were serving in close proximity. Virtually all of the Gestapo officers who organised deportations professed that they knew nothing of the intended fate of the Jews, and fell back on a variety of extremely vague cover stories. Ahlrich Meyer has dissected these in Taeter im Verhoer, a study of the interrogations of the members of the Befehlshaber der Sicherheitspolizei Frankreich, i.e. the Gestapo/SD in France.
Similarly, SS guards at Monowitz who were extradited to Poland disclaimed all knowledge of what was going on in Birkenau a few miles away. This was even more implausible, and was not a consistent claim, since some did admit knowledge, but anyone who was more than a stone's throw away from a killing site would routinely try to distance themselves from the events.
The 'no Nazi ever denied' argument is not really a conclusive one, because there are too many loopholes and exceptions through which their contemporary fanbois can weasel their way out.
The more relevant point is how many Nazis and SS men admitted knowledge and gave evidence. There were hundreds of them; too many for the usual obfuscatory arguments about torture or coercion to stand up to scrutiny, especially since there are statements made when SS men were at liberty. The classic example is Eichmann's interviews with Willem Sassen, who
wanted Eichmann to deny the Holocaust, but Eichmann refused to do so, when at liberty in Argentina before his capture.