א פרייליכן חנוכה
The Mechaber in Shulchan Aruch (O.Ch. 670 :2)
writes, "Chanukah was not instituted for משתה & שמחה".
The Rambam does write, that Chanukah is ימי שמחה והלל
The Brisker Rav writes that the Rambam meant with ימי שמחה
only to the extent that there is no Hesped & Ta'anis but
not that there is a Chiyuv Simcha.
According to the above, it would not be the appropriate greeting to wish someone "Happy Chanukah"
However according to the Taz who quotes from the
Maharshal, the Rambam does consider Chanuka as a
Yom Tov where משתה & שמחה are required.
Have a joyous & Lechtigeh Chanukah