Fred's fine (fingers still crossed).
After chasing Fred into the garden and spraying the front room, I left it for a while to settle.
Later, when I went to air the front room, I found several of my cats in the lounge even though the flap was locked both ways. They seem to have found a way of opening it; this might be because the magnetic strip has broken. So it's likely that Fred wasn't in the lounge when I did the spraying, just popped in afterwards.
He's eating, and is so far showing no signs of permethrin poisoning (twitching, vomiting, seizures).
I was loathe to contact VetsNow because I've had bad experiences with them in the past.
Thanks for the support.