A simple change.
A serious impact.
In the case of cosmetics, the manufacturer could choose ingredients that have been used for a long time, and so are likely to be safe. If the chemical is a new one, the first test could be the QSAR computer analysis to predict its likely irritancy.
In the next stage, a number of in vitro (test tube) tests could be used. Some tests are better than others for substances of a certain form, for example liquid rather than solid, and for substances of a certain chemical class, for example alcohols rather than oils. The aim would be to choose the best set of tests for a particular substance.
Doing more than one test is not a problem because in vitro tests are so much faster and cheaper than animal tests. For example, an Agarose Diffusion Test takes 24 hours per product, whereas a Draize test takes at least three days per product and costs 10 times more to carry out.
If the product is shown to be safe by this set of tests, it can then be trialed by human volunteers. This is the final and best test of all. By going through this series of steps products can be guaranteed to be safe without the suffering that is currently inflicted on animals.