The core mass of galaxy clusters is an important probe of structure formation. Here, we evaluate the use of a Single-Halo model (SHM) as an efficient method to estimate the strong lensing cluster core mass, testing it with ray-traced images from the `Outer Rim simulation. Unlike detailed lens models, the SHM represents the cluster mass distribution with a single halo and can be automatically generated from the measured lensing constraints. We find that the projected core mass estimated with this method, M$_{rm SHM}$, has a scatter of $8.52%$ and a bias of $0.90%$ compared to the true mass within the same aperture. Our analysis shows no systematic correlation between the scatter or bias and the lens-source system properties. The bias and scatter can be reduced to $3.26%$ and $0.34%$, respectively, by excluding models that fail a visual inspection test. We find that the SHM success depends on the lensing geometry, with single giant arc configurations accounting for most of the failed cases due to their limiting constraining power. When excluding such cases, we measure a scatter and bias of $3.88%$ and $0.84%$, respectively. Finally, we find that when the source redshift is unknown, the model-predicted redshifts are overestimated, and the M$_{rm SHM}$ is underestimated by a few percent, highlighting the importance of securing spectroscopic redshifts of background sources. Our analysis provides a quantitative characterization of M$_{rm SHM}$, enabling its efficient use as a tool to estimate the strong lensing cluster core masses in the large samples, expected from current and future surveys.
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