I, personally, do not observe Yom haShoah as a day of its own.
Aside from the mourning-in-Nisan issue, I follow what I heard Rabbi Yosef Dov Soloveitchik say, in his recorded Tishah b’Av talks: Tishah b’Av should be the day to commemorate the Holocaust. I grant that there are plenty of sources to show that Jews have, historically, observed other memorial days (such as 20 Sivan) for specific tragedies, but this is the view to which I gravitate.
However, I attend Yom haShoah programs anyway, because of a much bigger issue: The problem of a rabbi displaying his own unique practices in public.
I see three problems with public idiosyncrasy:
1: One rabbi’s personal quirks may inappropriately spread to others.
Example: I daven with a tallis over my head for most of the morning davening, and I know that others have started doing the same. I don’t know whether it’s emulation, or something they picked up on their own, but I worry if it’s emulation, because although I do it for personal concentration, I’m not sure the others understand it that way.
Another example: I have long wished to wear a tallis with the recently discovered murex techelet. I don't think it is proven, 100%, to be the right one, but there is no downside to wearing it even if it is wrong. However, I resist because it’s expensive, and I wouldn’t want others to think the expense obligatory because, “The rabbi wears it.”
2: One rabbi's quirks may inadvertently make others look bad.
To return to the earlier examples: What will people think of another rabbi who chooses not to wear a tallis over his head, or who doesn't wear techelet?
This issue is brought up in the gemara; it’s a concern called “laaz,” which translates loosely as “slander.” The gemara (Gittin 5b) talks about the case of Bar Hedya, who wished to be certified as a deliverer of gittin (billls of divorce):
Bar Hedya wanted to be approved to deliver gittin. He came to R’ Achi, the official responsible for gittin, who told him, “You must be present for the writing of every letter.”
He then came to R’ Ami and R’ Asi, who told him, “You need not do so. And if you should say, ‘I will practice stringently,’ you would slander earlier gittin!’”
So we don’t have a right to introduce stringencies which will make others look bad.
Note, though, that this concern for slander requires more nuance; it should not be a catch-all warning against public stringency.
In my class on Pesach regarding Machine Matzah and its early controversies, I noted that the Sanzer Rebbe (Divrei Chaim 24) argued vociferously against adoption of machine matzah, and rejected outright the concern that his insistence on using hand matzah would make others, who ate machine matzah, look bad.
The Sanzer brought several arguments, including:
• If others truly are not careful with mitzvot, I don’t need to worry that my care with mitzvot makes them look bad;
• The “slander” concern regarding a get is worse than in other areas of law, because it would result in children being mistakenly labelled “illegitimate.”
• The “slander” concern is not relevant if others are the ones who choose to deviate from the norm, and I maintain the norm.
3. Who are you to be quirky, anyway?
"Oh, he thinks he's Mr. Pious, wearing his tallis over his head like that for davening. Why, I remember when he..."
This is a concern for yuhara, which translates roughly to "arrogance" and "self-righteousness." This, too, is a talmudic concern, that one should not adopt practices which are identified with special piety, lest he seem to think too much of himself.
Or, to quote the classic punchline, "Look who thinks he's a gornisht!" (Google it, if you don't know the joke. It's out there.)
Again, nuance is required; the gemara does say that in certain cases one may adopt special practices, and ignore yuhara appearances, because his practices won't stand out or because his righteousness will encourage others to be righteous. (See, for example, Pesachim 54b.)
But, at bottom, this is another reason to avoid exhibiting unique halachic behavior in public.
So I try not to exhibit religiously quirky behavior (other types of quirky behavior are fine…) in public, I attend Yom haShoah programs, and it’s a small price to pay to avoid these three problems.