Light coming in from far enough off axis won't reflect into the focal plane. In this regard, most "light shrouds" actually make things worse by providing a surface for off-axis light to reflect off of on its way to the focal plane. No shroud = no reflecting surface.

A newtonian can be easily tested by looking into the focuser w/out an eyepiece. If all you see is black and the mirror, the scope is adequately baffled, and no shroud or tube will improve it.