The baseline hazard is usually estimated by the more straightforward Breslow or Kalbfleisch-Prentice methods

It is not statistically correct to remove "insignificant" variables, just as stepwise regression (without penalization) is invalid. Much has been written about this topic.

How exactly are you creating forecasts from this model? Are you using smoothing spline estimates of the Schoenfeld residuals to estimate the baseline hazard function? If so, do you do this before or after eliminating "insignificant" variables? If your goal is prediction, some very prognostic markers may have inference on hazards ratios which are not significant