For integrated dc-dc switching converter-based electrical networks, uniform or non-uniform current sharing of power lines is challenging in the presence of multiple time-varying disturbances within the converter systems, i.e., input voltage and load variations, and parameter uncertainties. This remains an open problem since existing methods commonly require additional inner control current loops, integrated circuits/components, and exhibit poor voltage regulation. This paper proposes a current sharing and disturbance rejection methodology formulated as a lightweight quadratic programming (QP) problem to mitigate errors of current sharing among the power lines. The method leverages a nonlinear control-affine model of parallel-connected converters, incorporating both matched (input voltage) and unmatched (load current) disturbances. We improve the method by adding disturbance-aware linear constraints into the design problem to mitigate the potential risk of thermal runaway and enhance system safety. Additionally, the current sharing problem is constructed as a safe control design problem within the control barrier function (CBF) framework. Further, the proposed method is decoupled from the feedback controller part so that the methods can be implemented in overall control architectures. The performance of the methods is demonstrated through comprehensive simulation studies on an unequal parallel-connected buck converter system. The hardware implementation of the proposed control systems is performed on a 10/20W parallel-connected buck converter system using a TMS320F28335 digital signal control board. The results demonstrate that the methods ensure the precise, uniform, and non-uniform current distribution.