Interesting comment on shaving soap from Franklin Soapworks
Don’t use the shampoo bar as a shaving soap. Any all-NaOH soap will not produce a proper shaving lather. You may be able to shave with it, but it is far from ideal.
A shave soap needs a large percentage of long-chain fatty acid content (preferably from direct addition of stearic acid or use of soy wax which is mostly tristearin) These produce dense creamy lather with small bubbles. Many artisan shave soap makers include a few percent coconut, but I feel it does more harm than good, encouraging big fluffy, unstable bubbles with high water content.
A good shave soap also needs some, but not a lot of unsaturated fats. Too much makes the lather slimy and unstable. Shea butter, mango butter, beef tallow, lard, castor, and avocado oil are the most-used sources of these. All but the last one also deliver stearic/palmitic acid content in addition to oleic and in the case of avocado, linoleic. They also deliver unsaponifiable content that makes for great post-shave feel.
The last condition for a shave soap is that it needs to be made with KOH lye. Generally between 60 and 100% of the lye content is KOH with the rest being NaOH. This produces a soap with higher water solubility. Without this, the soap will produce overly light fluffy lather that lacks necessary cushion. An ideal lather is dense, opaque, and gloppy and composed of extremely small bubbles. It contains much less water than you might expect. Finding the sweet spot is definitely part of the learning curve when starting to wet shave.
Because of the stearic acid normally used, shave soap generally has to be made as hot process since it turns into pasty, chunky glop as soon as lye is added. I have not tested it, but if using soy wax, it should be possible to run it as a cold-process.
“Taboos in the Shave Soap World”
-Olive oil and Bentonite Clay. There is a persistent bit of bad advice from soapmakers that adding bentonite clay to normal cold process soap makes it shave soap. This is a horrible idea. While bentonite clay can be responsibly used in a well-formulated shave soap to enhance slickness, it will in no way transform a normal bar soap. Since most small soapmakers have olive oil as their primary ingredient, it’s gotten a bad rap. It is absolutely possible to use it as a source of unsaturated fats in shave soap but it will be 10-30% of the batch and not the bulk of it. Plenty of stearic acid is needed to balance the performance.
-Melt & Pour. Several crafter/artisan oriented soapmaking supply companies resell melt and pour bases from SFIC, one of which is notably marketed as shave soap. While it isn’t the worst shave soap in the world, it is very mediocre and best avoided.
This is a pretty decent but not optimized starting place if you’d like to make your own shave soap: http://www.modernsoapmaking.com/the-best-wet-shaving-soap-recipe/
So far as I can tell, Franklin Soapworks doesn’t offer a shaving soap.