A one-shot algorithm called iterationless DANSE (iDANSE) is introduced to perform distributed adaptive node-specific signal estimation (DANSE) in a fully connected wireless acoustic sensor network (WASN) deployed in an environment with non-overlapping latent signal subspaces. The iDANSE algorithm matches the performance of a centralized algorithm in a single processing cycle while devices exchange fused versions of their multichannel local microphone signals. Key advantages of iDANSE over currently available solutions are its iterationless nature, which favors deployment in real-time applications, and the fact that devices can exchange fewer fused signals than the number of latent sources in the environment. The proposed method is validated in numerical simulations including a speech enhancement scenario.