In the case of a real free castling there is the possibility to also have castlings, wherein the king is making only one single step. Then an encoding as e.g. Kd1 is not sufficient to distinguish a castling move from a simple King's move. Moreover in traditional chess O-O and O-O-O is used. Thus the representation should be very related to that. using O-O-x has more common parts to those traditional forms than O-x. Thus I am preferring that.
By posting here I intended to investigate the status quo of writing down castling moves in variants, before I would start to implement such abilities in SMIRF's successor application Octopus.