Kinetic Monte Carlo (KMC) is a stochastic model used to simulate crystal growth. However, most KMC models rely on a pre-defined lattice that neglects dislocations, lattice mismatch and strain effects. In this paper, we investigate the use of a 3D off-lattice KMC algorithm. We test this method by investigating impurity diffusion in a strained FCC nanowire. While faster than a molecular dynamics simulation, the most general implementation of off-lattice KMC is much slower than a lattice-based algorithm. An improved procedure is achieved for weakly strained systems by precomputing approximate saddle point locations based on unstrained lattice structures. In this way, one gives up some of the flexibility of the general method to restore some of the computational speed of lattice-based KMC. In addition to providing an alternative approach to nano-materials simulation, this type of simulation will be useful for testing and calibrating methods that seek to parameterize the variation in the transition rates for lattice-based KMC using continuum modeling.