The detailed investigation of a superconducting spin-triplet valve is presented. This spin valve consists of a superconducting film covering a metal with intrinsic spiral magnetic order, which may be the result of a competitive exchange or of an asymmetric Dzyaloshinsky-Moriya exchange following from the central symmetry breaking of the crystal lattice. Depending on the anisotropy, this metal may change its magnetization either from a spiral to uniform order, as in Ho and Er, or in the direction of the spiral itself, as in B20 family crystals. Very recently, a new way of controlling the superconducting spin valve has been developed: the change of the magnetic order may also be triggered by magnonic relaxation processes, thus merging superconducting spintronics and magnonics. The nonuniform magnetic order controls the appearance of long-range triplet superconducting correlations (LRTC), which change the conditions of the proximity effect, enabling an external magnetic control of the superconducting critical temperature. We show that magnetic control of the spin-valve behavior can also be obtained for moderately low exchange energies thanks to an orientation-dependent averaging mechanism of the magnetic inhomogeneity on the scale of the Cooper pairs. The competition between these two mechanisms yields different behaviors of the spin-valve effect. Our numerical calculations show that at low exchange fields (as in MnSi) the spin valve effect may be quite significant. They suggest the switching behavior of the superconducting spin valve to be better optimized for B20 family compounds allowing magnonic control.