Leaded solder is safe to use if you wash your hands afterwards. Leaded solder - particularly 63/37 eutectic solder - is much more forgiving of poor technique. Lead-free isn't a massive inconvenience if you know what you're doing, but it can be absolutely infuriating for novices.

What about breathing the fumes? Also, doesn't (long-term) exposure to the fumes severely affect skin? I remember the folks soldering a lot of things for the Gemini and Apollo programs had very wrinkly, obviously damaged skin on their faces.

There is no lead in the solder fumes. If anything, lead-free solder is substanially worse, since the flux used for lead-free solder is a lot... harsher. Either way, this can be largely fixed by a small fume fan.

Thank you. In fact, I drive a small horizontal quadcopter propeller with a 3.7v LiPo while soldering to pull the fumes away.