Fortunately, you don’t have to do the searching yourself. The people that do the engraving look for knife materials that will engrave well. Not all stainless steel is suitable for laser engraving. Some steel is not consistent enough to give good results when you laser engrave it. It may be a great blade or handle component of a knife, as far as durability and appearance. But it might not be suitable for laser engraving.
Here are engravable knives, pocket knives that have been tested for engraving. They all have passed the test for beautiful laser engraving.