I would assume something/someone influenced Hawking to say that, it is completely illogical, and conveniently coincides with hollywood/movie lore. Speaking of Star Trek you should definitely watch STNG season 6 episode 12 "Ship In A Bottle". You'll probably get a kick out of that episode, definitely up your alley. Still a great series to watch after all these years I find myself watching re-runs on Netflix.
Possibly the explanation for the UFO observations coming at our own pace is due to our inability to describe such objects, lack of reference points. "Flying saucers" were depicted in the late 20s/early 30s sci-fi lore, before WW2. They were once described as "flying shields", even "chariots in the sky" very long ago, long before we had any type of flying craft. What is strange is the undeniable differences in these sightings like you had mentioned.. They are often cigar shaped, disk shaped, triangular, or even(as I've seen) plasma-like. Could this possibly suggest multiple different alien races visiting here? It's tough. Who is who? and is someone watching over us? My guess would be yes, something/someone is definitely is keeping us in line, somewhat.
There have been a number of incidents regarding nuclear weapons being disabled. We had established some type of agreement with the Soviets regarding such incidents, clarifying neither side was behind it. Without sounding too far fetched, I would dare to say something was watching closely, aware of the nuclear tensions. One of the best described here
https://www.youtube.com/watch?v=VgziDyPSUogI would say the "best" sighting in recent memory is the Phoenix Lights in 1997 -
https://www.youtube.com/watch?v=n0Q4J8_IahA - it was one solid object, massive, and over a big population zone. Kurt Russell by chance witnessed it himself flying into Phoenix. Even the governor of AZ at the time saw the object. Completely legitimate sighting imo, and covered up soon after as "military flares".
I do think there is more out there, and they are watching. But as mentioned before, I also think they are human, and this is why they are giving us so much attention. My gut tells me that they left the planet long ago, extinction-level event, and we're just the remnants left behind here that started over with little to nothing left of what was. Ancient technology and writings are very interesting stuff. I do believe Nazi Germany was well aware, as were our own scientists. There is without a doubt more to our past than is publicly known.