A vibratory fluid dispensing instrument holds a rheologically non-Newtonian (shear-thinning) liquid, gel, cream, or paste therapeutic composition in a container section of a disposable applying device from which the composition is manually dispensed into an applicator brush for application to one or more surfaces in an oral cavity. The instrument includes a vibratory appliance mounted to the device and mechanically coupled thereto to enable application of the composition in conjunction with mechanical energy that reduces the viscosity of the composition due to vibratory shear forces and thereby leads to better penetration of the composition into hard and soft tissue surfaces. The vibratory appliance can be separate from the applying device so that it can be removed from an applying device after the container section is empty and reused with a replacement applying device.