Let us begin with a translation of this passage from Galatiym as it is actually written in the Greek:

Galatiym (Galatians) 4:9-11:9-11
But now, do you not know YAHUAH, or rather are you not known by YAHUAH? How do you return again to the impotent and indigent ordered rudiments? Would you desire again to be in bondage? 10 You observe that day, and that month, and those occasions, and year by year. 11 I am afraid of you, lest I have bestowed upon you labour in vain."

This is essentially the same discussion we find in Colossians 2, discussing the vain deceits, philosophies of men, the rudiments and traditions, or in the Hebrew, the ta'akanoth and ma'asiym, which are specifically denounced in Matthew 23:1.

Paul (in the Hebrew: pa'al - worthy of a look) is not referring to the sacred feasts, but rather the "impotent and indigent ordered rudiments" such as the 9th of Av, birthdays, fertility feast days, (Valentines and Easter in the modern world), first days of the month, solstice celebrations, etc., none of which are mentioned in Scripture.

So, we return to the question of the day - shall those who have the testimony of Mashiach and who keep his commandments observe Chanukkah? Good question. Chanukkah is the Hebrew word often translated as "dedication". It first appears in the book of Bemidbar *(Numbers) at the dedication of the altar, and it reappears as a seven day feast in 2 Chronicles 7 when the altar of the temple was dedicated. Shalomah (Solomon) dedicated this altar on the 15th day of the seventh month which you might recognize as the feast called Cukkoth or Tabernacles. Chanukkah (named after Chanoch or Enoch, and meaning dedication) was not the name of the feast, but rather the statement of dedication of the altar.

In Makkabiym Sheniy (2 Maccabees) - a book found in the Septuagint, the Catholic Bible, the 1560 Geneva Bible, and the 1611 Authorized Version, we find the following verse:

Makkabiym Sheniy (2 Maccabees) 1:9
And now see that ye keep the Feast of Chanukkah in the month Kiclev.

In this same book, we find the following verse:

Makkabiym Sheniy (2 Maccabees) 1:18
Therefore whereas we are now purposed to keep the purification of the Temple upon the five and twentieth day of the month Kiclev, we thought it necessary to certify you thereof, that ye also might keep it, as the Feast of Chanukkah, and of the fire, which was given us when Nechemyah offered sacrifice, after that he had built the Temple and the altar.

Is there any other witness outside of Makkabiym? There sure is. In the Besorah Yahuchanon (the Gospel of John) Chapter 10:22-23 it reads as follows:

And it was at Yerushalayim the Feast of Chanukkah, and it was winter. 23 And YAHUSHA walked in the Temple in Shalomah's Porch. 

Cukkoth or Tabernacles is a fall feast, not a winter feast. This delineation stating that the feast was in the winter (in the Greek - χειμών cheimṓn) is a witness that this was not Cukkoth, but the feast initiated by the Makkabiym.

Don't ask the question WWJD (What Would Jesus Do)? Ask the question What Did Yahusha Actually Do (WDYAD)? The answer is: he kept the Feast of Dedication, the Feast of Chanukkah.