I am not using hydrogen peroxide, so tooth whitening cannot be illegal, can it?

Yes, it doesn't matter whether hydrogen peroxide or non-peroxide is used, it's a view confirmed by the High Court that tooth whitening is dentistry. Subsequently, even if you are using below the legal limit of hydrogen peroxide or a product which does not release hydrogen peroxide, you will still be breaking the law and putting your clients at risk. 

Products used by a dental professional have been thoroughly tested for many years and have been proven to work without being harmful to the teeth or gums. 

At best, other untested products that you may be using will not be effective and at worst, they could cause permanent damage.