you can make transparent soap using alcohol. i know a sugar solution is usually added too, but i dont know if its required.
i dont know if you can do it CP tho, it might need to be HP.
but you CAN do it from scratch
i have a library book out on it called "Making Transparent Soap: the art of crafting, molding, scenting & coloring"
i just skimmed the book so far, so i dont know much yet, but it does have recipes to make your own scratch transparent soap.
i came across this page in the past on how to make transparent soap:
http://curious-soapmaker.com/how-to-make-transparent-soap.html
heres a video with someone attempting to make melt & pour from scratch:
https://www.youtube.com/watch?v=AOVPvbwfscI
and here is another page on making melt & pour from scratch:
http://curious-soapmaker.com/how-to-make-melt-and-pour-soap-base.html
keep in mind that melt & pour frequently is transparent (but not always), but not all transparent soap is melt&pour. M&P means you can melt it to a liquid again....if you JUST make transparent soap, if you re-melt it, the transparency can go away and it wont melt to a nice smooth liquid like M&P does.
i have never attempted to make either transparent soap or M&P yet, this is just what i have seen on the web in the past and happened to have bookmarked.
i the book i have, they make totally transparent soaps from scratch
and i remember reading that the amount of alcohol you use is very important....too little will make your soap cloudy, and too much will ALSO make your soap cloudy.
and i also remember reading that the type of oil you use can determine how transparent the soap is....some oils do not get totally transparent even if you do the process for making transparent soap.
some of the recipes in the book use alcohol and glycerine both as the solvent
and some use just alcohol
they all use a sugar solution in the book