Extended X-ray Absorption Fine Structure (EXAFS) spectroscopy is a powerful technique that gives element-specific information about the structure of molecules. The development of a laboratory EXAFS spectrometer capable of measuring transmission spectra would be a significant advance as the technique is currently only available at synchrotron radiation lightsources. Here, we explore the potential of cryogenic detectors as the energy resolving component of a laboratory transmission EXAFS instrument. We examine the energy resolution, count-rate, and detector stability needed for good EXAFS spectra and compare these to the properties of cryogenic detectors and conventional X-ray optics. We find that superconducting tunnel junction (STJ) detectors are well-suited for this application.