There is no free alcohol in soaps, and it is added glycerine which makes it clear. You can do an internet search on "glycerine soap" and find a ton of info, as clear glycerine soaps have been known for over a century. The reason glycerine soaps arent used much is because glycerine is expensive. The myreth sulfate is just the sodium salt of the myristic acid (C14) ether sulfate, whereas the lauryl sulfate is the sodium ether sulfate of lauric acid (C12). Ether sulfates are stable and safe, and if I had to pick between the two, I would choose the lauryl sulfate every time, because of the benefits of the 12 carbon chain (see coconut oil forum). Dawn dishwash soap is predominantly ether sulfate, as are many shampoos in the US.
One seeking a non-irritating soap should consider those made from simple fatty acid carboxylates, which are buffered to a pH of about 6. Ivory.
If you wish to make your own soap, get "The Art of Soapmaking" by Merilyn Mohr. I used this years ago before going into the soap business, which I sold in 1982. It describes glycerine soap as well.