All over the world, especially in Western societies, table salt intake that is inordinately higher than the acceptable level has been observed. An excess of Na in the human diet, mostly from processed foods, is becoming the “number one killer”, leading to increased blood pressure. Therefore, the food industry is faced with a need to reduce Na in human nutrition in an effort to raise public health protection to a higher level. In this study, a commercially available combination of Na/K salts (COMB) at different concentrations was used as a NaCl substitute in the production of a modified, healthier, Na-reduced cheese. Samples of the modified low-Na white soft-brined cheese (WSBC) were produced by adding four different concentrations of COMB to production lots PL-1 to PL-4, and the control (CON) samples were prepared by salting with the usual, non-reduced concentration of NaCl. The effects of NaCl replacement on the physical–chemical parameters, major- and micro-elements, and microstructural and sensory properties of the WSBC were investigated. The obtained results indicated that there was no significant influence on the ash content, pH, and aw. The Na and K levels differed among treatments (p < 0.001). The lowest Na level in this study was recorded in PL-4 (only COMB was added) and was 334.80 ± 24.60 mg/100 g. According to the Na content, WSBC PL4 can be labeled with the nutrient claim “reduced amount of Na”. A significant difference (p < 0.05) was noticed in overall acceptance between the CON and PL-4, with no statistically significant difference found amongst other WSBC production lots. The replacement of NaCl resulted in a slightly greater firmness of the WSBC. The results confirm the possibility of producing low-Na WSBC when optimal amounts of a suitable mineral salt are used as a substitute for NaCl, thus reducing the risk of high Na intake in the human body through the consumption of evaluated cheese.