Ah, but both those procedures do exist separately in the
unitarian church.
A great many new members go through the process of expunging received beliefs from their spiritual systems, then gleefully revelling in the heady freedom of nose-thumbing a-gnosticism, and then begin to slowly collect things they do believe. maybe. kind of. transmogrified a bit. subject to change. There are a few unitarians born'n'raised, but the vast number (in north america) come to us after feeling rejected by or dissatisfied with or unfulfilled by other religions.
And unitarians are great ones for laying on of hands - not to heal, but literally. My church ends every service with everyone joining hands and singing "carry the flame of peace and love until we meet again". An ordination often (no two rituals are the same, though - unitarian churchs don't follow any prescribed procedures from above but do as they please within the loose boundaries of our principles) contains a laying on of hands, wherein the assembled people all squinch up in to the front of the church and lay hands on the person ahead of them, all centered on the newly ordained minister. naming & adoption ceremonies and weddings and funerals all have hand-laying and holding and shaking (mostly - we cut'n'paste our traditions to suit the occasion and the person), and coffee hour and random unitarian gatherings are bound to be dripping in hugs.
Unitarians are the most gregarious band of skeptics and rag-tag spiritualists you'll ever find, I bet.