Superconductivity in iron-based materials occurs in close proximity to a long-range ordered magnetic phase. In the iron pnictides, uniaxial pressure shifts the magnetic ordering temperature and increases the size of the magnetic moment near optimal superconductivity, suggesting enhanced quantum fluctuations [Tam et al., submitted]. FeTe, the parent compound of the Fe(Se,Te) system, forms a unique double-stripe magnetic order that is incompatible with superconductivity, but at higher energies the spin waves merge into the same form observed in superconducting Fe(Se,Te). Here we propose to study the spin wave evolution under uniaxial pressure in order to determine the energy scale of these two competing instabilities. The additional detwinning effect of uniaxial pressure in the low-temperature phase will also establish the instrinsic spin-wave parameters for the first time in this system.