We report on the second round of Chandra observations of the 3C snapshot survey developed to observe the complete sample of 3C radio sources with z<0.3 for 8 ksec each. In the first paper, we illustrated the basic data reduction and analysis procedures performed for the 30 sources of the 3C sample observed during the Chandra Cycle 9, while here, we present the data for the remaining 27 sources observed during Cycle 12. We measured the X-ray intensity of the nuclei and of any radio hotspots and jet features with associated X-ray emission. X-ray fluxes in three energy bands: soft, medium and hard for all the sources analyzed are also reported. For the stronger nuclei, we also applied the standard spectral analysis which provides the best fit values of X-ray spectral index and absorbing column density. In addition, a detailed analysis of bright X-ray nuclei that could be affected by pileup has been performed. X-ray emission was detected for all the nuclei of the radio sources in our sample except for 3C 319. Amongst the current sample, there are two compact steep spectrum radio sources; two broad line radio galaxies; and one wide angle tail radio galaxy, 3C 89, hosted in a cluster of galaxies clearly visible in our Chandra snapshot observation. In addition, we also detected soft X-ray emission arising from the galaxy cluster surrounding 3C 196.1. Finally, X-ray emission from hotspots have been found in three FR II radio sources and, in the case of 3C 459, we also report the detection of X-ray emission associated with the eastern radio lobe and as well as that cospatial with radio jets in 3C 29 and 3C 402.