Optical coherence tomography-based elastography (OCE) can perform localized, quantitative measurements of biomechanical properties. One of the most promising applications of OCE is to measure corneal stiffness, which has been linked to keratoconus, corneal crosslinking, and laser vision correction, and can help improve diagnosis, screening and treatment monitoring. Various techniques have been demonstrated to determine the speed of elastic waves traveling in the cornea and thereby to measure the shear modulus of corneal tissues. Here we present a new approach based on a contact probe with a piezo-electrically vibrating tip. This wave generation approach is robust, provides extensive control over the temporal and spectral profiles of the mechanical stimulus, and allows us to measure traveling wave velocities a frequency range of 1 to 15 kHz. The shorter wavelengths obtained at high frequencies can improve the resolution of traveling wave elastography and enable measurements of stiffer tissues such as the sclera. Direct contact with the corneal surface are routinely performed for intraocular pressure measurements, which suggest that this approach has a path to clinical translation. Interestingly, we found that mechanical stimulation tends to excite a combination of guided and non-guided elastic waves, which must be considered for accurate calculation of the shear modulus and may affect other OCT elastography techniques.