A few scattered comments:
For "cox" read "Cox" throughout: Sir David Cox, whose name you are using, is no relation, but I'm sensitive on that detail.
In principle, certainly you can bootstrap and see how much variability there is. But the
bootstrap command you might most naturally turn to expects you to work with named scalar quantities, most notably parameter estimates or figures of merit. So, you need to decide what results you want to focus on. There is no magic command that says "
bootstrap this and report on variability".
Your use of stepwise fitting through the
sw command is a matter of taste (which I don't share, but that is another story). But in principle doing things stepwise can only complicate your comparisons. Suppose different predictors are included in the final model in different replications; how are you going to handle that?
Cross-validation raises similar issues. In general terms, you would need to write much more code for that. If you are not an experienced Stata programmer, you are best advised to back off.
My reply, like your question, is sketchy and based mostly on general Stata experience.