To be honest, almost anything goes in a private recitation - even when praying in union with the Universal Church. If you were a priest and obliged to pray the LOTH, and in private omitted the signs of the Cross, you would still fulfill your obligation. The prayer itself is what we are taking part in, not necessarily the gestures. With that said, we can strongly say that such gestures are ancient, traditional, and highly recommended. We should be in communion with our fathers in faith, our contemporaries, and with those who are yet to come.
I myself often wonder if praying the Office as purely silent mental prayer still fulfills your LOTH obligation as a Priest or Religious brother/sister. The old pre-1971 Office required actual singing or audible recitation in order for it to be valid. I’m not sure if the new office requires anything in that way.
Are you using the 4-volume US Liturgy of the Hours? Tomorrow is the Memorial of Ss. Basil the Great & Gregory Nazianzen.
At the Office of Readings:
The Invitatory is “Christ is born for us, come let us adore Him.”
The Psalms are p. 765 (Friday Week I)
The Verse & First Reading is p. 533 (Isaiah 42:1-8)
second reading is p. 1285 (sermon of S. Gregory Nazianzen)
At Morning Prayer:
Psalms are 769
Reading is** 535**
Benedictus Antiphon is 1287
The rest you can figure out. Just remember that everything is from the Friday between January 2 and Epiphany, and from the feast of Ss. Basil & Gregory.