Given a weighted graph \(G = (V, E, \textbf{w})\) with some private edge attribute function \(f: E \rightarrow \mathbb {R}^{+}\) , the differentially private counting query problem aims to release the sum of the private edge attributes along a desired path (or set of paths) in G with differential privacy. In this work, we introduce the differentially private counting query problem on approximate shortest paths. A nearly-optimal algorithm with \(\widetilde{\varTheta }(n^{1/4})\) error is known for releasing the counting queries along all true shortest paths in G [6, 10]. We extend this result by showing if G admits a t-collective tree spanner with \(\eta _t\) spanning trees, then for each pair of vertices in V, we can release the counting query over a t-approximate shortest path with \(\widetilde{O}(\eta _t/\epsilon )\) additive error in the \(\varepsilon \) -DP case, and \(\widetilde{O}(\sqrt{\eta _t}/\epsilon )\) in the \((\varepsilon , \delta )\) -DP case. As an example of this, we use the collective tree \(O(k\log \log n)\) -spanner of [1] to give an algorithm which, for each pair of vertices, releases counting queries over a \(O(k\log {\log {n}})\) -approximate shortest path in G with \(\widetilde{O}(\sqrt{kn^{1/k}}/\epsilon )\) error. Our result is based on the polylogarithmic error in the differential private release of attributes along paths in trees, which is much lower than the \(\widetilde{\varOmega }(n^{1/4})\) error in the general case.