Well, conqueror is a pretty viable keystone already on katarina, since she can stack is relatively quickly and benefits a lot from healing/bonus damage.
As for AD>AP, I would still prefer to stick with AP, as although her AD ratios on average are higher than her AP, there's a couple of reasons that make AP better.
- All her AD scalings minus shunpo scales off of bonus AD, meaning base AD is not calculated
- You can get much more AP than you can AD
- Her daggers (which is her primary damage source) will eventually scale to 100% ap ratio, which is one of the best ratios in the game and is the same ratio as the Bonus AD scaling on her daggers, But you get more AP than you do AD meaning late game AP does much more damage.
- Her Q does not scale off of AD, and is kinda necessary for your Q to do damage in order to survive laning phase as it's your primary poke and way to get CS
- She doesn't synergize with many AD items as crit would be pointless, lethality is also quite pointless considering all her abilities do magic damage, last whisper and black cleaver are pretty useless as well as again, she does magic damage, and the only viable options for AD items on Katarina would be something like Death's Dance, or going a bit bruiserish and getting Steraks and such.
Overall, hybrid Katarina might sound good, but AP is just generally better and if you're planning on playing this in ranked I would stick with AP builds. However, there are some fun builds that can be tried going AD, perhaps a bruiser Katarina build.