... with blowing the fumes away you will avoid traces, but then you have all the fumes in the air, what's much more problematic.
Precoating the surface with a peel-off (I'm actually using sticking tape) helps for cutting, but it will give unpredictable results with engraving.
There are some more possibilities with bigger focal distances, but with this diodes I'm avoiding more than 30mm distance for better/smaller focus diameter and shape.
With the fiber-lasers I'll get up to 150mm focal distance and can remove the fumes without any traces -- but with the shorter distances with diodes it's all more like testing materials and best methodes for "complex" applications
Viktor