We report the evolution of a charge density wave (CDW) state in the quasi-2D rare-earth tritellurides (\(R\)Te\(_3\) for \(R\)=Er,Tm) as a function of in-plane uniaxial stress. Measurements of the elastocaloric effect, resistivity, and elastoresistivity allow us to demonstrate the importance of in-plane antisymmetric strain on the CDW and to establish a phase diagram. We show that modest tensile stress parallel to the in-plane \(a\)-axis can reversibly switch the direction of the ordering wavevector between the two in-plane directions. This work establishes \(R\)Te\(_3\) as a promising model system for the study of strain-CDW interactions in a quasi-2D square lattice.