The prediction of the risks of cancer and other late effects from space radiation exposure carries large uncertainties mostly due to the lack of information on the risks from high charge and energy (HZE) particles and other high linear energy transfer (LET) radiation. In our recent work new methods were used to consider NASA's requirement to protect against the acceptable risk of no more than 3% probability of cancer fatality estimated at the 95% confidence level. Because it is not possible that a zero-level of uncertainty could be achieved, we suggest that an acceptable uncertainty level should be defined in relationship to a probability distribution function (PDF) that only suffers from modest skewness with higher uncertainty allowed for a normal PDF. In this paper, we evaluate PDFs and the number or "safe days" in space, which are defined as the mission length where risk limits are not exceeded, for several mission scenarios at different acceptable levels of uncertainty. In addition, we briefly discuss several important issues in risk assessment including non-cancer effects, the distinct tumor spectra and lethality found in animal experiments for HZE particles compared to background or low LET radiation associated tumors, and the possibility of non-targeted effects (NTE) modifying low dose responses and increasing relative biological effectiveness (RBE) factors for tumor induction. Each of these issues skew uncertainty distributions to higher fatality probabilities with the potential to increase central values of risk estimates in the future. Therefore they will require significant research efforts to support space exploration within acceptable levels of risk and uncertainty.