Structured pruning reduces the inference cost of large language models (LLMs) by permanently removing neurons and weight rows, yielding dense, hardware-agnostic speedup. Existing post-training methods couple neuron selection and weight reconstruction through a shared calibration dataset, introducing domain bias and out-of-memory failures at high sparsity. We propose SARATHI, a framework that decouples these two stages. A data-free NMF Residual Subspace Probe scores neurons using intrinsic weight geometry, without accessing any calibration data, and carries a formal connection to Robust PCA. Adaptive OBS then reconstructs the pruned weights with a localized calibration batch, operating in 𝒪(d²) peak memory per layer and eliminating the global memory bottleneck of coupled methods. A Bias Shift Compensation step corrects systematic activation drift in post-LayerNorm architectures that would otherwise cause perplexity collapse at high sparsity. Experiments across six models from two architecture families (gated and non-gated FFN) at 15–40% sparsity show that SARATHI achieves competitive perplexity and matches or exceeds existing structured pruning baselines on zero-shot accuracy. Code: https://github.com/snkrbhr/SARATHI