We use direct numerical simulations of decaying primordial hydromagnetic turbulence with helicity to compute the resulting gravitational wave (GW) production and its degree of circular polarization. The turbulence is sourced by magnetic fields that are either initially present or driven by an electromotive force applied for a short duration, given as a fraction of one Hubble time. In both types of simulations, we find a clear dependence of the polarization of the resulting GWs on the fractional helicity of the turbulent source. We find a low frequency tail below the spectral peak shallower than the f(3) scaling expected at super-horizon scales, in agreement with similar recent numerical simulations. This type of spectrum facilitates its observational detection with the planned Laser Interferometer Space Antenna (LISA). We show that driven magnetic fields produce GWs more efficiently than magnetic fields that are initially present, leading to larger spectral amplitudes, and to modifications of the spectral shape. In particular, we observe a sharp drop of GW energy above the spectral peak that is in agreement with the previously obtained results. The helicity does not have a huge impact on the maximum spectral amplitude in any of the two types of turbulence considered. However, the GW spectrum at wave numbers away from the peak becomes smaller for larger values of the magnetic fractional helicity. Such variations of the spectrum are most noticeable when magnetic fields are driven. The degree of circular polarization approaches zero at frequencies below the peak, and reaches its maximum at the peak. At higher frequencies, it stays finite if the magnetic field is initially present, and it approaches zero if it is driven. We predict that the spectral peak of the GW signal can be detected by LISA if the turbulent energy density is at least similar to 3% of the radiation energy density, and the characteristic scale is a hundredth of the horizon at the electroweak scale. We show that the resulting GW polarization is unlikely to be detectable by the anisotropies induced by our proper motion in the dipole response function of LISA. Such signals can, however, be detectable by cross-correlating data from the LISA-Taiji network for turbulent energy densities of similar to 5%, and fractional helicity of 0.5 to 1. Second-generation space-base GW detectors, such as BBO and DECIGO, would allow for the detection of a larger range of the GW spectrum and smaller amplitudes of the magnetic field.