Intra-cortical brain-machine interfaces (iBMIs) have the potential to dramatically improve the lives of people with paraplegia by restoring their ability to perform daily activities. However, current iBMIs suffer from scalability and mobility limitations due to bulky hardware and wiring. Wireless iBMIs offer a solution but are constrained by a limited data rate. To overcome this challenge, we are investigating hybrid spiking neural networks for embedded neural decoding in wireless iBMIs. The networks consist of a temporal convolution-based compression followed by recurrent processing and a final interpolation back to the original sequence length. As recurrent units, we explore gated recurrent units (GRUs), leaky integrate-and-fire (LIF) neurons, and a combination of both - spiking GRUs (sGRUs) and analyze their differences in terms of accuracy, footprint, and activation sparsity. To that end, we train decoders on the "Nonhuman Primate Reaching with Multichannel Sensorimotor Cortex Electrophysiology" dataset and evaluate it using the NeuroBench framework, targeting both tracks of the IEEE BioCAS Grand Challenge on Neural Decoding. Our approach achieves high accuracy in predicting velocities of primate reaching movements from multichannel primary motor cortex recordings while maintaining a low number of synaptic operations, surpassing the current baseline models in the NeuroBench framework. This work highlights the potential of hybrid neural networks to facilitate wireless iBMIs with high decoding precision and a substantial increase in the number of monitored neurons, paving the way toward more advanced neuroprosthetic technologies.