Searches for signals at low signal-to-noise ratios frequently involve the Fast Fourier Transform (FFT). For high-throughput searches, we here consider FFT on the homogeneous mesh of Processing Elements (PEs) of a wafer-scale engine (WSE). To minimize memory overhead in the inherently non-local FFT algorithm, we introduce a new synchronous slide operation ({\em Slide}) exploiting the fast interconnect between adjacent PEs. Feasibility of compute-limited performance is demonstrated in linear scaling of Slide execution times with varying array size in preliminary benchmarks on the CS-2 WSE. The proposed implementation appears opportune to accelerate and open the full discovery potential of FFT-based signal processing in multi-messenger astronomy.