OK you are no chump. But apparently I am - never heard of a CKD diet - fascinating.
Are you a bodybuilder? Or some other kind of athlete???
If there is one thing I would claim to be expert on its oils. I'm not a big cook, but these are the oils I would stick to:
1. Butter (preferably grass fed)
2. Olive oil (extra virgin)
3. Coconut oil
4. Flax seed oil (cold processed, stored in opaque container and refrigerated) - eat in moderation.
Can you possibly use olive oil in Mayo? Failing that how about something like Udo's Choice or some Flax? The important thing is that you shouldn't heat it. Also try and eat it fresh as whipping it up will cause it to oxidize. How does that sound?