This paper presents SHTNet, a lightweight spherical harmonic transform (SHT) based framework, which is designed to address cross-array generalization challenges in multi-channel automatic speech recognition (ASR) through three key innovations. First, SHT based spatial sound field decomposition converts microphone signals into geometry-invariant spherical harmonic coefficients, isolating signal processing from array geometry. Second, the Spatio-Spectral Attention Fusion Network (SSAFN) combines coordinate-aware spatial modeling, refined self-attention channel combinator, and spectral noise suppression without conventional beamforming. Third, Rand-SHT training enhances robustness through random channel selection and array geometry reconstruction. The system achieves 39.26\% average CER across heterogeneous arrays (e.g., circular, square, and binaural) on datasets including Aishell-4, Alimeeting, and XMOS, with 97.1\% fewer computations than conventional neural beamformers.