You mean the wording is essential in determining the infallibility of the declaration? Could you give an example of the “wording”?
It needs to be made clear that a teaching doesn’t have to be proposed in an exercise of Papal infallibility in order for it to be infallible. I don’t think you want the thread to get sidetracked into a discussion of infallibility, and indeed I’m not qualified to provide a deep, technically precise answer. This article might help… I have to admit that it quickly gets over my head:
catholicity.com/encyclopedia/i/infallibility.html
A clear example of the exercise of the charism of Papal infallibility is given in
Ineffabilis Deus, in which Pope Pius IX wrote:Accordingly, by the inspiration of the Holy Spirit, for the honor of the Holy and undivided Trinity, for the glory and adornment of the Virgin Mother of God, for the exaltation of the Catholic Faith, and for the furtherance of the Catholic religion, by the authority of Jesus Christ our Lord, of the Blessed Apostles Peter and Paul, and by our own: “We declare, pronounce, and define that the doctrine which holds that the most Blessed Virgin Mary, in the first instance of her conception, by a singular grace and privilege granted by Almighty God, in view of the merits of Jesus Christ, the Savior of the human race, was preserved free from all stain of original sin, is a doctrine revealed by God and therefore to be believed firmly and constantly by all the faithful.” But that formula isn’t a requirement.
Here’s another that seems to fit the bill:Since St. Francis, up to this time, has not been named the Patron of Writers in any solemn and public document of this Apostolic See, We take this happy occasion, after mature deliberation and in full knowledge, by Our Apostolic authority, to hereby publish, confirm and declare by this encyclical, everything to the contrary notwithstanding, St. Francis de Sales, Bishop of Geneva and Doctor of the Church, to be the Heavenly Patron of all Writers.
And yet another:Then after earnest prayers for light: "In honor of the Holy and Undivided Trinity, for the glory of the Catholic Faith, by the authority of Jesus Christ, of Peter and Paul, and by our own authority, after mature deliberation and at the request of the Cardinals, Patriarchs and Bishops, We declared that the professed nun of the Order of Discalced Carmelites, Thérèse of the Child Jesus, was a Saint and was to be inscribed in the calendar of the Saints, memory of her to be kept on October the third of each year.