We’ve already covered this with the anointing rituals of PCS 121-125. There are a few differences. PCS 137 contains a note to omit the general intercessions, as they are folded into the litany of the sick:
137. The liturgy of the word is celebrated in the usual way according to the instructions in no. 134. The general intercessions are omitted since they are included in the litany.
In the homily the celebrant should show how the sacred text speaks of the meaning of illness in the history of salvation and of the grace given by the sacrament of anointing.
A brief period of silence may follow the homily.
The litany of the sick is a bit different from what is given in the rite of anointing outside of Mass. The option to shorten or adapt remains:
138. The priest may adapt or shorten the litany according to the condition of the sick persons.
Let us pray to God for our brothers and sisters and for all those who devote themselves to caring for them.
Bless N. and N. and fill them with new hope and strength: Lord, have mercy. Lord, have mercy.
Relieve their pain: Lord, have mercy. Lord, have mercy.
Free them from sin and do not let them give way to temptation: Lord, have mercy. Lord, have mercy.
Sustain all the sick with your power: Lord, have mercy. Lord, have mercy.
Assist all who care for the sick: Lord, have mercy. Lord, have mercy.
Give life and health to our brothers and sisters on whom we lay our hands in your name: Lord, have mercy. Lord, have mercy.
The litany of the sick would be a priority for a musical setting, I would think, above all other parts of the anointing ritual.
Some instructions for laying hands, and either blessing oil or saying a prayer of thankgiving. This is very similar to what is used in anointing outside of Mass:
139. In silence, the priest lays hands on the head of each sick person. If there are several priests present, each one lays hands on some of the sick.
140. The priest says a prayer of thanksgiving over blessed oil or he may bless the oil himself (see PCS 21), using one of the following:
141. The priest anoints the sick person with the blessed oil. If there are large numbers of sick people to be anointed, other priests may assist the celebrant. Each priest anoints some of the sick, using the sacramental form as described in no. 124.
142. The priest says one of ther prayers A-D, as in no. 125.
I didn’t post the texts of these prayers when I blogged on PCS 125. The A, B, C, and D options are two general prayers (one addressed to the Father, one to Christ), one for severe or terminal illness, and one for advanced age. The first three seem most appropriate to the large group setting of anointing at Mass.