We present a catalog of low-mass dense cores observed with the SHARC-II instrument at 350{mu}m. Our observations have an effective angular resolution of 10'', approximately 2.5 times higher than observations at the same wavelength obtained with the Herschel Space Observatory, albeit with lower sensitivity, especially to extended emission. The catalog includes 81 maps covering a total of 164 detected sources. For each detected source, we tabulate basic source properties including position, peak intensity, flux density in fixed apertures, and radius. We examine the uncertainties in the pointing model applied to all SHARC-II data and conservatively find that the model corrections are good to within ~3'', approximately 1/3 of the SHARC-II beam. We examine the differences between two array scan modes and find that the instrument calibration, beam size, and beam shape are similar between the two modes. We also show that the same flux densities are measured when sources are observed in the two different modes, indicating that there are no systematic effects introduced into our catalog by utilizing two different scan patterns during the course of taking observations. We find a detection rate of 95% for protostellar cores but only 45% for starless cores, and demonstrate the existence of a SHARC-II detection bias against all but the most massive and compact starless cores. Finally, we discuss the improvements in protostellar classification enabled by these 350{mu}m observations.