Remember, you can check the full document Paschale Solemnitatis on this site, among many on the internet.
A Word service should be celebrated in the absence of a priest:
31. Where the Mass cannot be celebrated, there should be a celebration of the word of God on the theme of the Lord’s messianic entrance and passion, either on Saturday evening or on Sunday at a convenient time. (Cf. Roman Missal, Passion Sunday (Palm Sunday), 19)
Though it seems that a procession is not provided in this instance. How would you interpret this, other than a sigh of relief for avoiding a significant liturgical production?
Back to the procession …
Music is proposed:
32. During the procession, the choir and people should sing the chants proposed in the Roman Missal, especially psalms (22)and (45), as well as other appropriate songs, in honor of Christ the King.
That first psalm is associated with the “Why have you abandoned me,” but its later verses are a hymn of praise. Given that Psalm 45 is for a royal wedding (Note its use on Assumption) I would take these choices to be more suggestive of the praise of Christ. New Testament texts might include the kenosis hymn of Philippians 2, or any of the other canticles used in Evening Prayer.