This is what I’ve found.
From the Book of Blessings
1626 The blessing of throats may be given by a priest, deacon, or a lay minister who follows the rites and prayers designated for a lay minister. If the blessing is conferred during Mass, the blessing follows the homily and general intercessions, or, for pastoral reasons, the prayer of blessing may take the place of the final blessing of the Mass. When the blessing is given outside Mass, it is preceded by a brief celebration of the word of God. If the blessing is to be celebrated at Morning Prayer or Evening Prayer, it is given after the reading and responsory (and homily) and before the gospel canticle.