According to the Revised GIRM ...
The Lord's Prayer
81. In the Lord's Prayer a petition is made for daily food, which for Christians means preeminently the eucharistic bread, and also for purification from sin, so that what is holy may, in fact, be given to those who are holy. The priest says the invitation to the prayer, and all the faithful say it with him; the priest alone adds the embolism, which the people conclude with a doxology. The embolism, enlarging upon the last petition of the Lord's Prayer itself, begs deliverance from the power of evil for the entire community of the faithful.
The invitation, the Prayer itself, the embolism, and the doxology by which the people conclude these things are sung or said aloud.
The Rite of Peace
82. The Rite of Peace follows, by which the Church asks for peace and unity for herself and for the whole human family, and the faithful express to each other their ecclesial communion and mutual charity before communicating in the Sacrament. As for the sign of peace to be given, the manner is to be established by Conferences of Bishops in accordance with the culture and customs of the peoples. It is, however, appropriate that each person offer the sign of peace only to those who are nearest and in a sober manner.
HOWEVER there is a codicil entitled: " Adaptations Within the Competence of Bishops and Bishops' Conferences". I find nothing in here that says anything about raising hands or hugging people. You decide ...
Adaptations Within the Competence of Bishops and Bishops' Conferences