Network coordinates (NCs) enable the efficient and accurate estimation of network latency by mapping the geographical relationship among all nodes to Euclidean space. Many researchers have proposed NC-based strategies to reduce the lookup latency of distributed hash tables (DHTs). However, these strategies are limited in the improvement of the lookup latency; the nearest node to which a query should be forwarded is not always included in the consideration scope of a node. This is because conventional latency improvement strategies assign node IDs independent of the underlying physical network and still have the possibility of detour routing. In this paper, we propose an NC-based method of constructing a topology-aware DHT by Proximity Identifier Selection (PIS/NC). PIS/NC constructs a logical ID space of a DHT from the Euclidean space constructed by NCs; a node ID corresponds to the network coordinate of the node. By doing this, the consideration scope of a node always contains the nearest node, thus, we can expect a great reduction in lookup latency. Unlike the conventional PIS strategy that poses unavoidable issues due to uneven ID distribution, PIS/NC tries to moderate these issues by a simple optimization, provided by a PIS/NC stabilizer. The PIS/NC stabilizer detects an uneven distribution of node IDs locally, and then recalculates some IDs so that the unevenness is moderated. As case studies, this paper presents Canary and Harpsichord, which are PIS/NC-based CAN and Chord, respectively. Simulation results show that PIS/NC-based DHTs improve lookup latency. Under the environment using the Transit-Stub model, where SAT-Match and DHash++ are only able to reduce the median lookup latency by 19% of CAN and 9% of Chord, respectively, Canary and Harpsichord reduce it by 40% and 35%, respectively. We also verify that the PIS/NC stabilizer moderates the non-uniform distribution of node IDs.