According to Chris Lintott's twitter the Feb show is planned (some of the filming for it was probably done some time back) and will have Dr Lucie Green on as well.
I mention her as I suspect if the BBC did decide to keep the Sky at night going they may well want to 'BBCize' it with at least one regular female presenter and she'd be a good choice as she's often on the show anyway.
You mention a female presenter and one who immediately springs to mind who used to have a higher profile a few years ago than nowadays is Heather Couper
who I always found an engaging character who knew her stuff.
Another female who would tick two PC aspects for the BBC, being a woman, and black, not to mention very clever, and who I have discovered only relatively recently and enjoyed is Dr Maggie Aderin Pocock
, who has presented some astronomy items, clearly qualified and would in no way be a token gesture, or case of positive discrimination.
Sir Patrick clearly looked like he had been training Chris Lintott for a number of years with a view to succeeding him, but for me I cannot see him as "the presenter".
Of course these are all busy people in their own right, and even if offered the chance might not want, or be able to take it up.