We present a statistics-aware compression strategy that processes photon timestamps directly from time-correlated single-photon counting (TCSPC) modules for time-domain fluorescence lifetime imaging (FLIM). Rather than storing or transmitting the full histogram per pixel, timestamps are projected onto sparse, non-uniform one-dimensional spline sketches, with knot positions optimally allocated based on Fisher information. This knot allocation concentrates sketch channels where the decay signal exhibits the greatest statistical discriminability, rather than using a uniform allocation. The proposed approach is extensively validated on synthetic mono- and bi-exponential decay data and on experimental fluorescent dye data, demonstrating comparable accuracy to full-histogram non-linear least-squares fitting (NLSF) and Poisson maximum-likelihood estimation (MLE) at compression ratios of up to 256x. We further validate the feasibility of integrating the timestamp-to-sketch projection directly into firmware via fixed-point (FXP) lookup-table (LUT) simulation, targeting high-spatial-resolution single-photon avalanche diode (SPAD) arrays subject to significant data-throughput constraints.