No, this is not ok. It should be done, preferably by a deacon, but can also be done by a priest, or if nothing else, by the priest-celebrant.
This is found at usccb.org/liturgy/goodfriday.shtm
The second form of the adoration of the cross which takes place at the door of the church, in the middle of the church and before entering the sanctuary has not changed (GF, no.16).
The priest or deacon may then carry the cross to the entrance of the sanctuary or another suitable place (GF, no.17).