Beli-type soaps are essentially undiluted KOH soap pastes. They are softer than bar soaps made with NaOH, but their innate softness is the chief difference. Hence, in my opinion, Beldi-type soaps do not require a preservative, any more than bar soaps do.
The benchmark rule covering the need for preservatives is whether a product contains water.
Some soapmakers might contend that water would likely be introduced into Beldi-type soaps stored in jars, during use, and this might be a valid argument for using a preservative. On the other hand, bar soaps contain some residual water content as well and also get wet during use, but do not require a preservative. The high pH of both types of soaps protects them from bacterial contamination.
KOH soap pastes are the basis for making liquid soaps, which are made by diluting KOH soap pastes sufficiently to make liquids, and many soapmakers believe that liquid soaps should include a preservative since liquid soaps have very high water content. Personally, I feel that liquid soaps offered for sale should contain a preservative. (I use 5% Liquid Germall Plus.) I do not add a preservative to my Beldi-type soaps that are offered for sale since I feel a preservative is unnecessary--but that is just my opinion.
Beldi soaps that I have made are generally stored for about a year at room temperature before they are used up, and I have never seen or smelled any sign of spoilage or rancidity.
Since many Beldi-type soaps include unusually high levels of super fats, I would say that if you are going to have an issue, it would be rancidity. There are several ways to protect against this. One is to include super fats that protect against rancidity, such as meadowfoam oil. Another is to include Vitamin E blended with the super fats. A third method is to include rosemary oleoresin blended with the super fats.
The bottom line here is that I can't give you a definite answer, and you will have to be guided by your own judgment in this matter.