When using a Hand Saw (or Hack saw), Dust hides line
Painter here.  I stock quality throwaway brushes (Redtree Fooler) and I find them all the time in the wood shop next to saws. 

The woodshop guys use paint brushes to dust off woodwork.

A chip brush is a "cheapie" natural bristle paint brush. They are ideal for chasing chips.  The 2" width is the most popular amongst the woodworkers and metalworkers.  Expect to pay $1-1.50 retail for generic cheapies. 

Being natural bristle, they hate latex paint. They work fine for alkyds, and are ideal for 2-part coatings (LPU) where cleaning the brush is out of the question.  We win awards with em.