Praise be to Allah.
Congratulating the kuffaar on their festivals is haraam, as
you say. Please see question no. 947
It seems that sending a message to those of them who you
know, on the day of their festival, saying “I wish you well” or “I wish you
all the best” is a kind of congratulations.
But if you send this message on a day other than their
festival, with the intention of calling them to Islam and hoping that they
will be guided, there is nothing wrong with that.
It was narrated that Abu Moosa said: The Jews used to sneeze
in the presence of the Prophet (peace and blessings of Allaah be upon him),
hoping that he would say to them, “Yarhamakum Allaah (may Allaah have
mercy on you).” But he would say, “Yahdeekum Allaah wa yuslihu baalakum)
(may Allaah guide you and reform you).”
Narrated by Imam Ahmad (19089), Abu Dawood (5038) and
al-Tirmidhi (2739); classed as saheeh by al-Albaani in al-Irwa’
It says in ‘Awn al-Ma’bood: i.e., he did not say to
them “Yarhamakum Allaah (may Allaah have mercy on you)” because mercy
is only for the believers; rather he prayed for them as was appropriate,
that they be guided and enabled to believe.
There is nothing wrong with praying for a kaafir to be guided
aright, rather it is proven that this is the Sunnah of the Prophet
(peace and blessings of Allaah be upon him).
And Allaah knows best.