The classical disjoint shortest path problem has recently recalled interests from researchers in the networks planning and optimization community. However, the requirement of the shortest paths being completely vertex or edge disjoint might be too restrictive and demands much more resources in a network. Partial disjoint shortest paths, in which a bounded number of shared vertices or edges is allowed, balance between degree of disjointness and occupied network resources. In this paper, we consider the δ-vertex k edge-disjoint shortest path problem (δV-kEDSP), that is, for a pair of distinct vertices in a network graph, it optimally finds k edge-disjoint shortest paths between them where at most δ vertices are shared by at least two paths. We present techniques for exactly solving δV-2EDSP with runtime O(δm+n log n), which significantly improves the O(mn^2+n^3\log n) runtime bound of the state-of-art. The proposed theoretical approaches are also validated by computer experiments on both synthetic and real networks which demonstrate their superior efficiency of up to three orders of magnitude faster than the state-of-art solution.