The growing demand for smart home interfaces has increased interest in non-intrusive sensing methods like vibration-based gesture recognition. While prior studies demonstrated feasibility, they often rely on complex preprocessing and large Neural Networks (NNs) requiring costly high-performance hardware, resulting in high energy usage and limited real-world deployability. This study proposes an energy-efficient solution deploying compact NNs on low-power Field-Programmable Gate Arrays (FPGAs) to enable real-time gesture recognition with competitive accuracy. We adopt a series of optimizations: (1) We replace complex spectral preprocessing with raw waveform input, eliminating complex on-board preprocessing while reducing input size by 21x without sacrificing accuracy. (2) We design two lightweight architectures (1D-CNN and 1D-SepCNN) tailored for embedded FPGAs, reducing parameters from 369 million to as few as 216 while maintaining comparable accuracy. (3) With integer-only quantization and automated RTL generation, we achieve seamless FPGA deployment. A ping-pong buffering mechanism in 1D-SepCNN further improves deployability under tight memory constraints. (4) We extend a hardware-aware search framework to support constraint-driven model configuration selection, considering accuracy, deployability, latency, and energy consumption. Evaluated on two swipe-direction datasets with multiple users and ordinary tables, our approach achieves low-latency, energy-efficient inference on the AMD Spartan-7 XC7S25 FPGA. Under the PS data splitting setting, the selected 6-bit 1D-CNN reaches 0.970 average accuracy across users with 9.22 ms latency. The chosen 8-bit 1D-SepCNN further reduces latency to 6.83 ms (over 53x CPU speedup) with slightly lower accuracy (0.949). Both consume under 1.2 mJ per inference, demonstrating suitability for long-term edge operation.