When you say brief handling, (check water, temps, etc) do you actually handle him during these times, or are you just opening the cage & not picking him up each time?
You got him 4 days ago, & he's a baby, he's probably just stressed from being moved to a new home.
Kings tend to be flighty, especially as babies, & often eventually grow out of it & can be handled no problem.
It's generally recommended to leave babies alone for a week, with no actual handling, or feeding. Babies stress a lot easier than adults do. You defintely want to leave him alone for two days after feeding, otherwise he might regurge.