In bulk non-centrosymmetric magnets the chiral Dzyaloshinskii-Moriya exchange stabilizes tubular skyrmions with a reversed magnetization in their centers. While the double-twist is favorable in the center of a skyrmion, it gives rise to an excess of the energy density at the outskirt. Therefore, magnetic anisotropies are required to make skyrmions more favorable than the conical spiral in bulk materials. Using Monte Carlo simulations, we show that in magnetic nanowires unusual skyrmions with a doubly twisted core and a number of concentric helicoidal undulations (target-skyrmions) are thermodynamically stable even in absence of single-ion anisotropies. Such skyrmions are free of magnetic charges and carry a non-integer skyrmion charge s. This state competes with clusters of s = 1 skyrmions. For very small radii, the target-skyrmion transforms into a skyrmion with s < 1, that resembles the vortex-like state stabilized by surface-induced anisotropies.