The geometric hitting set problem is one of the basic geometric combinatorial optimization problems: given a set of points and a set of geometric objects in the plane, the goal is to compute a small-sized subset of that hits all objects in . Recently Agarwal and Pan (2014) presented a near-linear time algorithm for the case where consists of disks in the plane. The algorithm uses sophisticated geometric tools and data structures with large resulting constants. In this paper, we design a hitting-set algorithm for this case without the use of these data-structures, and present experimental evidence that our new algorithm has near-linear running time in practice, and computes hitting sets within 1.3-factor of the optimal hitting set. We further present dnet, a public source-code module that incorporates this improvement, enabling fast and efficient computation of small-sized hitting sets in practice.