Hawking, I believe, is referring to a more metaphorical 'hovering'. As light, or anything, approaches the event horizon, it becomes more and more redshifted---it's motion appearing to go slower and slower and slower, approaching zero apparent velocity to an outside observer (approximately) infinitely far away. Anything falling into a BH, thus appears to end up 'hovering' just outside of it.
From the perspective of the object falling into the BH, or an observer traveling nearby/similarly to it, nothing special happens. To the infalling observer, time still seems to pass normally... everything is the same. So there is no problem with the electromagnetic wave itself behaving (basically) normally as it approaches the blackhole.
There are lots of questions and material about this and related subjects on physics.stackexchange which might be helpful.
Aside: Apologies for the extremely pedantic and unhelpful comments you received on your question.