As mentioned by Ali, you will need to follow your country's laws.
I will just say as both a seller and a buyer (I do buy soap from other makers), that dealing with MP is a bit of a conundrum. As a buyer, if I only saw the cold process ingredients I wouldn't buy it. However I have bought soap that had an ingredient list that included "soap embed made from MP base" or something like that, and it did not deter me from purchasing. I will not buy if there is no effort made to acknowledge that the embed is not the same ingredients as the rest of the soap. That said, I see even big name soapmakers like Royalty Soaps do not appear to be disclosing the melt and pour ingredients in the soap label. If she did, she would also have ingredients such as: Sorbitol, Propylene Glycol (made from vegetable glycerine), Sorbitan Oleate (Emulsifier), Oat Protein. (This is from the exact MP base she says she uses, the low sweat clear from TKB.) And that's just one of many reasons why I will not buy from her anymore.
As a maker, and obvs feeling the way I do about the above... I do list my ingredients like this from one of my soaps that uses an MP embed on top, I have highlighted the embed ingredients for you:
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This has made me a bit more cautious about the MP that I purchase too.
If a customer is concerned, I tell them they can remove the embed before using but the embed is such a small amount of the soap, and soap is a washoff product that any kind of risk outside of allergies is extremely unlikely. If they are still concerned.... then I suggest that they place a custom order of that fragrance without the embed, lol. I don't do embeds on all my soaps (right now I have two out of 20 soaps with embeds) so I also try to find a different soap for the customer.