Two separate tickets may be a flag with Cathay who may not let her board in the first place because of the TWOV issue.
FT is littered with threads about people having issues wih TWOV - in some cases caused by airlines not wanting to take the risk of fine for possibly landing an ineligible person.
They will take the most cautious approach which may just be 'deny' even though an immegration officer would allow it.
One option is buy a return - which would reduce the costs - with a long return date which you then forget about or plans changed ...