The present study aimed to investigate the impact of practicing sports activities on manual skills, focused on reaction time depending on manual laterality. The objectives of the study were to identify the differences in improving simple, optional, and cognitive reaction times in the manual executions of student athletes who practice team sports involving the manual handling of the ball (volleyball, basketball, handball) in comparison with student athletes who practice individual sports and with non-athletic students; to identify the differences regarding the reaction time of the right- and left-handed executions depending on the manual lateralization of the subjects (right- and left-handedness) between the three experimental samples: team sports group (TSG), individual sports group (ISG), and the group of non-athletes (NAG) through the use of computer tests. The study included 335 subjects who were divided into three groups: TSG with 102 subjects, ISG with 112 subjects, and NAG with 121 subjects. The subjects of the study were given five computer tests to evaluate three types of reaction time: simple reaction time (Start/Stop Test), choice reaction time (Check Boxes Test, Hit-the-dot Test), and time of cognitive reaction (Trail making Test part A and B). The results were analyzed regarding right- and left-handedness, as well as the execution hand (right hand or left hand) in solving the tests. The results of the study highlighted significant statistical differences between the three groups: TSG, ISG, and NAG. The best results were recorded by TSG in all tests, and the lowest by NAG. Statistically significant differences were also recorded between the executions with the dominant hand compared to the executions with the non-dominant hand in relation to right- and left-handedness. The study highlighted that the smallest differences in all the study groups were recorded in the simple reaction time test, where the differences between the right-handed and left-handed executions were the lowest, reflecting the best level of symmetrization of the motor executions.