Machine Learning models are getting more accurate, yet their complexity and opacity are also increasing. Explainable AI improved their general interpretability by quantifying the contributions of input features to predictions. Despite these advancements, practitioners still seek to gain causal insights into the underlying data-generating mechanisms. To this end, a possible solution is to rely on classical probabilistic causal analysis, which offers tools to quantify causal effects. However, causal analysis assumes a sufficient knowledge of causal structure, which is often unreachable from data alone. Indeed, causal discovery algorithms produce, at most, partial causal structures, namely Completed Partially Directed Acyclic Graphs (CPDAG). The conventional approach involves fully orienting the structure with exogenous causal knowledge through expert interaction or real-world experiments. In this paper, we focus on quantifying a specific total causal effect. Within this context, we emphasize that a partial structure can be sufficient to answer the query, and can be reached by different sequences of additional causal knowledge. Whether coming from an expert or an experiment, each addition has a cost difficult to assess a priori. The contribution of this paper is twofold: given a CPDAG and a specific query, we identify a set of irrelevant edges, and we introduce an algorithm for ranking the remaining informative edges, providing a guide to iteratively obtain a partial structure sufficient for resolving the query. Simulations show that these two contributions significantly reduce the number of requests for exogenous causal information, corroborating the feasibility of a causal impact quantification with very limited exogenous information.