How exactly do the Klingons justify using cloaking ships, a strategy which necessarily involves sneaking up on an enemy and catching them unaware? Wouldn’t sneak attacks conflict with their notion of honour?

As another Klingon points out, the only honour is in victory.

The Klingon code of honour is pretty flexible, and there seem to be a lot of different interpretations of it. Some more dogmatic Klingons, like Worf, might find it dishonourable, and avoid cloaking if they can, but there are other Klingons who are less adherent to tradition, and would freely make use of cloaking as they wished.