//Is it plausible that the judge would agree a 'no case', where there is no direct evidence of 'murder'? Or more likely that it would be considered a jury matter?//
From your description it's highly probable that the judge would decide there is no case to answer. A bigger question might be on what basis did the prosecuting authorities decide to prosecute? If there is no direct evidence (i.e. no eye-witnesses, no forensic evidence and the alleged victim is dead) why did they pick the defendant to prosecute? Evidence of a propensity towards online sex-chatting (if it was admitted) is scarcely sufficient to support a charge of murder. It has shades of Christopher Jefferies:
https://www.theguardian.com/tv-and-radio/2014/dec/07/-sp-peter-morgan-christopher-jefferies-tv-drama-joanna-yeates
OK, Mr Jefferies did not make it to court but the media and the police had him in the frame on a basis of no evidence whatsoever. It was hardly surprising there was no evidence as he had not committed the crime, but he was stood up purely on the basis that he had habits and a demeanour which some people viewed as a little strange.