From my experience I have noticed that the time that I will unmold and cut the soap loaf (most of the times these steps are happening one right the other one), will greatly depend on two factors as long as the recipe is a balanced one with the 3 major oils (palm, coconut, olive).
1) The water amount of the recipe and
2) the environmental temperature.
The 1) is easy to understand as a more concentrated lye solution will saponify a little faster the oils and will give less moisture in the soap so you must cut sooner as it will be less elastic in a sorter period of time.
The 2) will also influence how soon the saponification will happen after the trace and upon molding, as heat encourages saponification, where gel phase (if it happens) will also speed things up even more.
My own way of determining the time to unmold and cut will be by using my finger to press on the soap loaf. If there is a very slightly dent on my finger's spot then it will be the time to cut.
If a recipe is not balanced (eg. 100% Coconut Oil - saturated fatty acids) then the time of cutting is usually sooner. The 100% Olive oil recipe (monounsaturated fatty acids) might be cut a little later than normal if there are similar temperature conditions.
The saturated fatty acids are responsible for the sooner cutting as they saponify usually sooner and they are a straight line in a molecular level that give hardness in a soap bar a little easier / sooner too.
But for the fact that in the recipe with 100% CO we usually use a little more water than normal (30% lye concentration), and in the 100% fresh OO we can use use less water than normal (36 - 40% lye concentration) the time for cutting might be similar.
