Starting from your proposed solution I would suggest the following simplification. A single GeoGraphics can produce the desired output and handles everything related to the projection. In version 10.0.2 GeoProjectionData also has the "Hammer" (or Hammer-Aitoff) and "Aitoff" projections.
rad = Import["~/Downloads/DadosRad2014_RADECVELOC_15124_1024.dat"];
p = Cases[rad, {a_, b_, c_} -> {b, Mod[a, 360, -180]}];
GeoGraphics[{Red, PointSize[0.01], Point[GeoPosition[p]]},
GeoRange -> All, GeoProjection -> "Sinusoidal",
GeoGridLines -> Automatic, GeoGridLinesStyle -> Directive[Dashing[{.01, .005}], Green],
GeoBackground -> Black
]
