Please bear in mind, when choosing a brand, that as a business owner you are legally responsible for performing "due diligence" to ensure the safety of a product.
Regardless of if a product range is accredited by an insurance company. IMHO, having spoken to several, they don't have much of a clue and their policies, I was told be their underwriters, are written in such a way to avoid responsibility if the product is not compliant.
Why would a product not be compliant if it is registered on the Submit Cosmetic Products Notification (SCPN) portal? Well, perhaps the specific product is not actually registered.... or the information used to register it is false i.e. it contains ingredients not specified in the SDS or on the product label. Perhaps because the factory in China is dishonest.
If your client sues, don't expect the insurer to support you. They will support the claimant, to avoid paying out. So it will be up to you to demonstrate that you did due diligence, are trained in the specific product and applied the product exactly as the manufacturer stated, which includes using the manufacturers UV lamp.
But if they analyse the product and find undeclared ingredients, ingredients in amounts that are different from the SDS, are still using a MSDS and not an SDS, or find disturbing reports online of other injuries, perhaps even from Educators of the brand, then you will become personally liable, irrespective if your company is a Ltd or not.
One advice that I would give anyone starting a business, is before you think of ways to make money, think of ways that you can lose it. Protect yourself first and use that as a foundation to build a strong business. Unfortunately, too many in this industry are swayed by price, the possibility have hundreds of colours and glitzy brand social media. Instead of building a rock solid and unique reputation for your education and skills in your own region, combined with safe products from a brand with a longterm reputation.