Assuming you plan on letting it evolve using Insurgence’s delta evolution conventions:
Deltas evolve in a similar way to their normal evos, like if a normal mon evolves by stone, the delta will always use a stone as well. If a mon evolves by level, the delta evolves at the same level. If a mon evolves by happiness at day, the delta could evolve via hate at night. A mon that evolves via level will never evolve with a trade, so on, so fourth.
Since normal skitty evolves via moon stone, it’d have to use a stone of it’s own, like a sun stone or fire stone, most likely without the “lower than half” prerequisite that you mentioned.