Well, technically there's no such thing as a 'safe day' in terms of using no protection whatsoever. You can get pregnant while on your period, you can get pregnant from pre-cum even if he pulls out, etc. There's less fertile days - so you'd be fine using one form of protection instead of two, so if you're on the pill/implant you can get away with not using a condom - but the only way you can have unprotected sex with a 0% chance of getting pregnant is if you or your partner are infertile.
Just remember that stress affects your hormonal cycle - the more stressed you are, the later your period will be. (In the run up to my exams, I had no period for three months, and then it came two days after my last exam...) So even if you're not pregnant, your period might carry on being late because you're worrying about it. I agree that there's a fairly low chance in this case - low fertility and pulling out before ejaculation - but best to take a pregnancy test just in case. If your period still doesn't come, take another one a week or so later just to be sure.