Near-infrared spectroscopy has proven to be a valuable method to monitor tissue oxygenation and haemodynamics non-invasively and in real-time. Quantification of such parameters requires measurements of the time-of-flight of light through tissue, typically achieved using picosecond pulsed lasers, with their associated cost, complexity, and size. In this work, we present an alternative approach that employs spread-spectrum excitation to enable the development of a small, low-cost, dual-wavelength system using vertical-cavity surface-emitting lasers. Since the optimal wavelengths and drive parameters for optical spectroscopy are not served by commercially available modules as used in our previous single-wavelength demonstration platform, we detail the design of a custom instrument and demonstrate its performance in resolving haemodynamic changes in human subjects during apnoea and cognitive task experiments.