If the procession and blessing takes place outside Mass, I suspect that really any form you use can be considered a "popular devotion", and there would be no problem with using a Processionale of your choice, or for that matter, a rite of your own composition. What constitutes a "solemn procession" in the OF is not a question I am qualified to answer, but surely we all need more processions in our lives.

When you've worked out an order, would you care to share it with us? I imagine that several folks would like to take up such a tradition for Christmases to come.

I'm not sure how apropos this is/was, but one Christmas Eve I remember the priest using the Book of Blessings to bless the creche (the prayer in the USCCB link above), except he adapted the first line of that second paragraph to read: "Lord, bless + this manger and all who look upon it..." Again, that may not conform exactly to the letter of the law, but it did make clear that it was the manger scene being blessed.

I wonder if there is something in the Personal Ordinariate and/or Anglican Use rituals available.

Caleferink, the action of blessing (making the sign of the cross with the hand) was left out the blessings contained in The Book of Blessings (sometimes disparagingly called the Book of Well Wishes by priests because of the seeming lack of blessings compared to the old Roman Ritual). The Congregation for Divine Worship and the Discipline of the Sacraments responded stating that the action of blessing should always be made when blessing an item/object, cf. AAS 94 (2002): 684. The core of the decree states:

Since, from the established usage, the liturgical custom has always been in force that in the rites of blessing the sign of the cross is employed by being traced by the celebrant with the right hand over the persons or things for whom mercy is implored, this Congregation for Divine Worship and the Discipline of the Sacraments, in order to dispel any doubts, has established that, even if the text of the part of the Roman Ritual entitled "The Book of Blessings" remains silent about the sign itself or lacks an express mention of the appropriate time for this action, nevertheless the sacred ministers should adopt the aforementioned sign of the cross as necessary when carrying out any blessing.

Without a mention, however, the appropriate time should be regarded as when the text of the blessing uses the words blessing, to bless, or similar or, lacking these words, when the prayer of blessing itself is concluded.

The difficulty—which you allude to—is that many (if not all) of the "blessings" contained in the Book of Blessings are not blessings of objects but rather a request for God's blessing upon the people present. It's an odd thing—and I think most priests adapt the blessings in just the way you mention (e.g., "Lord, bless + this manger and all who look upon it..."). It's something I hope will be changed when a new translation of the Book of Blessings is published.

We will be using the following:

The Liturgy begins:
The Procession
Please stand.

Priests and ministers enter.
When all is prepared, the Proclamation of the Nativity is sung.

Then the deacon sings:

D: Let us go forth in peace
R: In the name of Christ. Amen.

Hymn
(example: Angels, from the realms of glory)

The Blessing of the Crib
P: Today, you shall know that the Lord will come to deliver you.
R: And at sunrise you shall behold his glory.

P: Our help is in the Name of the Lord.
R: Who has made heaven and earth.

P: The Lord be with you.
R: And with your spirit.

P: Let us pray.
P: Almighty and everlasting God, who did cause thine only-begotten
Son to come down from heaven, and as on this night to be born of the
blessed and glorious Ever- Virgin Mary for our salvation: vouchsafe,
we beseech thee, so to bless and hallow this Crib, wherein are shown
forth the wonders of that sacred Birth; that all they, who beholding
the same shall ponder and adore the mystery of his holy Incarnation,
may be fulfilled with thy heavenly benediction unto life eternal.
Through the same Christ our Lord.

Hymn
(Example: O come, all ye faithful)

At the High Altar
D: Blessed is he that comes in the name of the Lord.
R: God is the Lord, who has shown us light. Alleluia.

Collect
D: Let us pray.
D: Almighty God, who has given us thy only-begotten Son to take our nature
upon him, and to be born of a pure Virgin: Grant that we being
regenerated, and made thy children by adoption and grace, may daily be renewed
by thy Holy Spirit; through the same our Lord Jesus Christ, who lives and
reigns with thee and the same Spirit, ever one God, world without end.
R . Amen

Mass begins

Ceremonial:
Traditionally Marian banners of Mother and Child are carried during the procession.
The procession is divided into 2 parts. The first and shorter part processes towards the crib. After the baby Jesus has been laid in the manger and the crib blessed, the procession resumes sung to the second hymn and ends at the foot of the altar for the collect.
For the procession, the priest is normally vested in cope. After the second collect, the priest changes to a chasuble, and the introit is sung. The altar is incensed during the introit antiphon. If there is more than one thurible, only one thurible is used to incense the altar as usual, while the others may be swung chain length at the foot of the altar.