Unity Week starts on Thursday January 18 and ends on January 25.
Before the 1960s, January 18 was the Feast of the Chair of S Peter at Rome (while February 22 celebrated his Chair, that is to say, his episcopate, in Antioch).
In the Good Old Days, the Wantage Sisters ... who now comprise our Ordinariate Sisters in Birmingham, the praying heart of the Ordinariate, as our Ordinary puts it ... used to publish an annual ORDO "... in strict accordance with the Use of the Western Church". This was widely used both in Anglo-Papalist churches and in Anglo-Catholic churches generally. The latest one I possess is 1969. Before January 18, the following information is printed:
CHURCH UNITY OCTAVE BEGINS
Ad lib, during the Octave: one 2cl Vot M For the Unity of the Church. Cr (on Sunday only), Common Pref (pref Trin on Sunday). P[urple]
This will undoubtedly have been lifted from what was authorised for Roman Catholics in England, Scotland, and Wales on the very eve of the liturgical alterations of the late 1960s. What it means is that it is lawful to say daily one Mass of the Votive for Christian Unity (Ad tollendum Schisma if your Missal, like mine, is pre-1962; but the texts are the same in the 1962 Missal) on the Sunday within the Octave (even if it be Septuagesima); and also on each of the weekdays, because they are all (even the Conversion of S Paul) days occupied by III class feasts and so admit Second Class Votives. No Gloria, of course.
My own suggestion would be to start the Octave with a (permitted) Votive Mass of the Chair of S Peter on January 18 (Mass as on February 22 except that the Alleluia is said) and to conclude with the Mass for S Paul on January 25. It was the idea of linking up the two Apostles which gave rise to the Octave.
Alleluia for the Chair of S Peter: Alleluia, alleluia. Tu es Petrus, et super hanc petram aedificabo ecclesiam meam. Alleluia.
I have thought it worth while providing this information because I do not think it is in the available Extraordinary Form ORDOs in English or French.
The same Mass for Unity, of course, is provided for use in Liturgical English in the Ordinariates. The rubrics make clear that it can be said on any day except Solemnities, the Sundays of Advent, Lent, and Easter, All Souls, Ash Wednesday, Ember Days, Rogation Days, weekdays of Holy Week and of the Easter and Pentecost Octaves. Such votives ARE allowed BUT ONLY FOR "a real necessity or pastoral advantage" on Obligatory Memorials and the weekdays of Advent, Christmastide, Lent, and Eastertide. Pretty permissive, eh?