About 30%-40% of classical novae produce dust 20-100 days after the outburst, but no presolar stardust grains from classical novae have been unambiguously identified yet. Although several studies claimed a nova paternity for certain grains, the measured and simulated isotopic ratios could only be reconciled, assuming that the grains condensed after the nova ejecta mixed with a much larger amount of close-to-solar matter. However, the source and mechanism of this potential post-explosion dilution of the ejecta remains a mystery. A major problem with previous studies is the small number of simulations performed and the implied poor exploration of the large nova parameter space. We report the results of a different strategy, based on a Monte Carlo technique, that involves the random sampling over the most important nova model parameters: the white dwarf composition; the mixing of the outer white dwarf layers with the accreted material before the explosion; the peak temperature and density; the explosion timescales; and the possible dilution of the ejecta after the outburst. We discuss and take into account the systematic uncertainties for both the presolar grain measurements and the simulation results. Only those simulations that are consistent with all measured isotopic ratios of a given grain are accepted for further analysis. We also present the numerical results of the model parameters. We identify 18 presolar grains with measured isotopic signatures consistent with a CO nova origin, without assuming any dilution of the ejecta. Among these, the grains G270_2, M11-334-2, G278, M11-347-4, M11-151-4, and Ag2_6 have the highest probability of a CO nova paternity.