Not really sure tbh, for LCY my instinct would be weekdays just because the airport doesn't operate on the Saturday afternoon onwards, and only restarts some time on Sundays (more knowledgeable people will know exactly when). Which is we we get those somewhat unusual EDI/GLA-EAS direct flights etc, because the aircraft have to be doing something.....

Good luck and have fun, I suppose these things are never entirely risk free when you're dealing with separate bookings, I seem to recall KARFA (hardly a newbie at travel) has some epic tale from Los Angeles or thereabouts involving midnight buses between airports, so I guess always good to have at least an inkling of a plan B anyway. I imagine the tickets you book will have "Free Change On Day" as they are simple returns and unlikely to be the cheapest ones, so if it all unravels early on, you might be able to use that feature to save at least something by pushing them out to later?