Yesterday I facetiously posted about Friday penance during the Octave of Christmas.
Days (other than Sunday) within the Octave of Christmas are not “heavy enough” (as a “solemnity” would be) to “outweigh” the Friday obligation to do some sort of penance as determined by the conferences of bishops. In the 1962 Missale Romanum they are “II class”, which corresponds to the newer, non-traditional calendar’s “feast”. In the 2001 Missale Romanum they are categorized as second class, as “feasts”. If, howeverm you are at a parish named “Holy Innocents”, such as that great place in Manhattan, and the Feast of the Holy Innocents falls on the Friday, you might argue that it is greater due to it being the patronal feast.
Bottom line, the Octave of Christmas does not have the “weight” of the Octave of Easter.
So, pay attention to can. 1251.
Can. 1251 Abstinence from meat, or from some other food as determined by the Episcopal Conference, is to be observed on all Fridays, unless a solemnity should fall on a Friday. Abstinence and fasting are to be observed on Ash Wednesday and Good Friday.
And, you can ask your parish priest to dispense you or commute your act of penance.
Can. 1245 Without prejudice to the right of diocesan bishops mentioned in can. 87, for a just cause and according to the prescripts of the diocesan bishop, a pastor[parish priest] can grant in individual cases a dispensation from the obligation of observing a feast day or a day of penance or can grant a commutation of the obligation into other pious works. A superior of a religious institute or society of apostolic life, if they are clerical and of pontifical right, can also do this in regard to his own subjects and others living in the house day and night.
You can substitute another form of penance for abstaining from meat. Make it penitential, however. Abstinence from meat has good reasoning behind it. For some, however, there abstinence from other things can be of greater spiritual effect.