Minor lore discrepancy, but the Widow is a geth design that they make a huge deal out of having such hard recoil that it would shatter an organic's arm if they tried to fire it, not unlike the Claymore shotgun is only comfortably shot by krogan.
Yes, they change things around in ME3 with codex justifications, but the point still stands that prior to ME1, there's no contact with the Geth and their technology isn't in the galaxy at large. The Widow simply wouldn't be present in this timeline.
Besides, if I remember right, it weighs 38 kilos. You do NOT want to carry that around.