IGEdgeSelect[function_, property_][g_] := With[{selection = EdgeList[ g, _?(Function[edge, Not@function@PropertyValue[{g, edge}, property]])]}, EdgeDelete[g, selection] ]
g = CompleteGraph[5, EdgeStyle -> {1 <-> 2 -> Green, 3 <-> 4 -> Green}]
g // IGEdgeSelect[# === Green &, EdgeStyle ]