Can people who are not (and cannot be) brothers and sisters wish each other Happy Raksha Bandhan without tying Rakhis?
People like friends, lovers, spouse etc.
Raksha Bandhan is not based on any religious scriptures, but from an incident in indian history, symbol of platonic relation. So long the individuals involved are true to their intentions in core of their heart, it can extend beyond boundaries of blood relation.
Some stories are told on the origins of this raksha bandhan in hindu mythology, however, they do not stand technical scrutiny (Goddess Laxmi & King Bali, Lord Krishna & Drapaudi). Mythological instances are possible, however, the symbolic thread wrapping is not.