Is it permissible to say 'Shalom Aleichem' to a mourner?

Is the prohibition of greeting a mourner also applicable to saying 'Shalom Aleichem', which does not inquire about their well-being?

'Shalom Aleichem' is considered the same as greeting a mourner.

Gemara Moed Katan, page 21b: "During the first three days, greeting is forbidden? For it was taught: An incident occurred where Rabbi Akiva's sons died, and all of Israel entered and delivered a great eulogy. At the time of their departure, Rabbi Akiva stood on a large bench and said: Our brothers, the house of Israel, listen! Even two sons of a bridegroom are comforted for the honor you have shown. And if you came for Akiva's sake - there are many Akivas in the market. But you said: The Torah of his God is in his heart, and all the more so your reward is doubled, go to your homes in peace. - The honor of the multitude is different." And the Ritva wrote there: "And we learn from here that even such language is forbidden to a mourner, and not only actual inquiry about well-being, as many thought." And the Rema wrote: "There are those who are lenient nowadays in greeting a mourner after 30 days, and they have no reason, unless to say that what we practice is not called greeting as in their days." And the Magen Avraham wrote, Siman 554, SK 21: "It is written in Yoreh De'ah, Siman 385, that this greeting we give is not called greeting as in their days, and this requires study, for in the Tur there it brings the Jerusalem Talmud, which explicitly writes 'Shalom Aleichem', and also in the Gemara it says to greet a student to a rabbi 'Shalom Aleichem, Rabbi', and therefore one should not be lenient."