Coconut oil, along with palm kernel (natural or hydrogenated/flakes), babaçu, murumuru, is a
lauric oil, i. e. high in lauric and myristic acid, and MCT fatty acids.
People who are
specifically allergic against coconut come along with replacing CO by other lauric oils.
People who (like OP, if I understood you correctly) want to avoid lauric oils for their
drying/stripping/irritant action, only lose time with rotating through lauric oils. Though very helpful for lathering, solubility and cleaning action, lauric oils are not necessary for a satisfactory soap experience.
The steps I care about for a non-lauric soap recipe, that still is great performing (some have already be mentioned):
- Dual lye: replace 5–10% of NaOH by KOH (with adjusted amounts of course)
- Use aloe vera juice or rice porridge instead of water
- Add sorbitol/sugar/honey
- Castor oil at 5–8%
- You'll notice that, without lauric oils, the “hardness” and “longevity” numbers of soap calculators are identical. I like recipes around 25–35 of these numbers best (higher and the soap becomes too insoluble and “stone like”. Your calculator might warn you that they would be too soft (when in doubt, unmould a few hours later than usual)
- You might aim around 15% linoleic acid, no less than 10%. (That's a personal quirk of me, but I found that PUFAs add a pleasant “slip” to non-lauric soaps, and their conditioning properties offset some of the stripping action of CO even with low superfat). Keep in mind rancidity issues, have your chelators and antioxidants at hand.
- Balanced palmitic/stearic ratio around 1:1. Too palmitic-heavy, and the soap might not become hard enough in reasonable time; too stearic-heavy can feel chalky and is slow-lathering
ETA:
most other oils are made 10% max
I'm sorry? Never heard of this “rule”, and it sounds like advice given to beginners to prevent them lose time on trying to run before they can walk.
The authoritative measure for a soap recipe is the final fatty acid profile. How you end up there is secondary. There are indeed oils that qualify as base oils and others don't. But reducing the “>10% oils” to palm, olive, and coconut would make many soapers very unhappy
.