Infallible statement == A statement given which cannot be incorrect (it is not fallible).
Infallible action == An action which cannot be incorrect
Infallible discipline/teaching == A discipline/teaching which cannot be incorrect.
Thus, either Holy Days of Obligation are infallible, or it’s possible the RCC has it wrong. Those are the only two options.
So, are Holy Days of Obligation infallible (that is, necessarily correct [for whatever reason], and thus impossible to be changed in the future without committing error), or is there a possibility of error (meaning that the RCC is not infallible in its teaching magisterium)? If the former, all one has to show is a single Holy Day of Obligation that has been changed.
It is a really strange construction to speak of Holy Days of Obligation as “infallible”. The two words just don’t go together.
Starting with your definitions, you defined infallible statement satisfactorily, it is a teaching of the Church that it is a charism of the the Pope. “Infallible action” just seems odd. No one who knows the doctrine of papal infallibility would ever speak of an infallible action. Sinlessness is called impeccability, and the pope does not possess this (no matter how much of a great guy i think he is

). I disagree with you in lumping together “infallible discipline” and “teaching”. Under the Catholic understanding of infallibility, “teaching” goes along with “statement”, and disciplines are never infallible.
Holy Days of Obligation are a discipline, and thus, cannot be spoken of as “infallible”. When imposed by the legitimate authority, however, they are binding upon the faithful, until such time as they are revoked or loosed. Let’s look deeper. What are the HDOs?
1 Jan: Solemnity of Mary, Mother of God
6 Jan: Epiphany
19 March: Solemnity of St. Joseph
Thursday after the 6th week of Easter: Ascension
Thursday after Trinity Sunday: Corpus Christi
29 June: Solemnity of Sts. Peter and Paul
15 Aug: the Assumption of the Blessed Virgin Mary
1 Nov: All Saints
8 Dec: Immaculate Conception
25 Dec: Nativity of the Lord
This is the full list given by canon law, which may be cut by individual bishops. As you can see, there are a few that commemorate specific events, like the Epiphany or the Assumption, we could potentially speak of those days being “infallibly proclaimed” in that the pope could come out and tell us that those are the actual days that those things happened (he has not done so). Some other days, however, like the Solemnity of Mary, Mother of God, or Corpus Christi (aka, the Body and Blood of Christ), or All Saints, do not commemorate specific events, but rather celebrate certain people (Mary, Jesus, the rest of the saints). For these days, it would not be proper to speak of them as “infallible” in any sense, since the day does not and cannot correspond with any event.
There is the potential (at least grammatically) to say that the decree saying you must go to church on these days is infallible, but this falls outside of the Church’s definition of papal infallibility.
You seem concerned that the Church could be wrong in requiring the faithful to attend church on these days. Why?