Special curves in the Minkowski space such as Minkowski Pythagorean hodograph curves play an important role in computer-aided geometric design, and their usages are thoroughly studied in recent years. Bizzarri et al. (2016) introduced the class of Rational Envelope (RE) curves, and an interpolation method for G1 Hermite data was presented, where the resulting RE curve yielded a rational boundary for the represented domain. We now propose a new application area for RE curves: skinning of a discrete set of input circles. We show that if we do not choose the Hermite data correctly for interpolation, then the resulting RE curves are not suitable for skinning. We introduce a novel approach so that the obtained envelope curves touch each circle at previously defined points of contact. Thus, we overcome those problematic scenarios in which the location of touching points would not be appropriate for skinning purposes. A significant advantage of our proposed method lies in the efficiency of trimming offsets of boundaries, which is highly beneficial in computer numerical control machining.