In noncentrosymmetric superconductors (NCSs), the inversion symmetry (IS) is most commonly broken by an antisymmetric spin-orbit coupling (SOC). Removing the spin degeneracy and splitting the Fermi surface (FS) into two branches. A two component condensate is then produced mixing an even singlet and an odd triplet. When the triplet and the singlet strengths are comparable, the pair potential can have rich nodes. The angular line nodes (ALNs) are associated with the point group symmetries of the anisotropic lattice structure and they are widely studied in the literature. When the anisotropy is weak, other types of nodes can be present which then affect differently the low temperature properties. Here, we focus on the weakly anisotropic NCSs and the line nodes which survive in the limit of full isotropy. We study the topology of these radial line nodes (RLNs) and show that it is characterized by the Z(2) index similar to the quantum-spin-Hall Insulators. From the thermodynamic perspective, the RLNs cause, even in the topological phases, an exponentially suppressed low temperature behaviour which can be mistaken by nodeless s-wave pairing, thus, providing an explanation to a number of recent experiments with contraversial pairing symmetries. In the rare case when the RLN is on the Fermi surface, the exponential suppression is replaced by a linear temperature dependence. The RLNs are difficult to detect, and for this reason, they may have escaped experimental attention. We demonstrate that Andreev conductance measurements with clean interfaces can efficiently identify the weakly anisotropic (WA) conditions where the RLNs are expected to be found.