Reaction between a vinegar/salt/hydrogen peroxide mixture as an etching solution and copper I am looking for the less harmful chemical solution to serve as an etching solution. After many searches, my interest went to a vinegar/salt/hydrogen peroxide solution.

I have to ask then if the residue of this solution is harmful and if it is ok to pour it in the regular water waste system.
The etching solution itself is fine to dispose of down the drain. However, if you use it to etch copper, the dissolved copper ions are quite toxic, and should not be disposed of through the sewer system. 

You can bypass the problem by collecting the etch solution, and submerge aluminum foil. $$\ce{3Cu(CH3COO)2(aq) + 2Al(s)-&gt;2Al(CH3COO)3(aq) +3Cu(s)}$$React with the aluminum until the bluish color disappears, then collect the solid copper + remaining aluminum to throw in the trash. You can now flush the solution down the drain.