Positive HPV16. Will remove CIN1 with laser. How can I have a safer sex next time with partner? Condom all the time for him? What about me?

Maybe no need. It is likely you had HPV16 for several months before CIN was diagnosed. If regular sex during that time, you can assume your partner is already exposed and likely infected and there's no point in precautions now. For a new partner, consistent condoms will help but frankly not much. Partners can be vaccinated, but you're beyond recommended age. Most couples just don't worry about HPV.