Don't lick your boards, wash your hands before you eat, and if you're really concerned, wear gloves while handling solder wire.
The smoke from soldering isn't lead - a soldering tip is (if it's not literally glowing into the yellows) far, far too cold to vaporize any lead from solder - you need to be 1500+C for it to start being a problem, and you're not soldering that high. It's rosin smoke, and if you're in doubt, leave your iron in a puddle of solder - it shouldn't smoke, it should just sit there liquid after the initial rosin has burned off.
The rosin smoke isn't great, but it's not a lead toxicity issue.
Your concern is lead on your hands from the wire, and then eating afterwards without a good scrubbing. I don't think it will penetrate your skin, but you could always wear a pair of gloves if you wanted. There are some shooting sports soaps that are designed to help really rip any lead off your hands, so you might use one of those if you're concerned.
Also, afaik, there's no reason for hobbyists to not always use lead-free solder. But of course that doesn't mean something you're taking apart used lead free.
The leaded solder melts easier than non-leaded. This is good because you are way less likely to burn off traces or melt the board using a lower temperature iron. I only use leaded solder because I suck at soldering.
Repairing an old device that used leaded solder is a reason to use leaded solder (even new leaded solder during the repair). I don't even use the same tips across leaded and lead-free solder.
I think pretty much all consumer electronics uses lead free solder for the last 10+ years. The reason hobby users tend to use leaded is it's much easier to work with and they don't care about health or the environment that much.
A few years back spent a lot of time stripping lead paint using a heat gun and IR emitter thing ("silent paint remover"). It was definitely smelly, but I convinced myself that the temperatures were far too low to vaporize lead.
But in the back of my mind I always wondered if there was an equivalent of a eutectic mixture for the liquid/vapor phase transition.
The smoke from soldering isn't lead - a soldering tip is (if it's not literally glowing into the yellows) far, far too cold to vaporize any lead from solder - you need to be 1500+C for it to start being a problem, and you're not soldering that high. It's rosin smoke, and if you're in doubt, leave your iron in a puddle of solder - it shouldn't smoke, it should just sit there liquid after the initial rosin has burned off.
The rosin smoke isn't great, but it's not a lead toxicity issue.
Your concern is lead on your hands from the wire, and then eating afterwards without a good scrubbing. I don't think it will penetrate your skin, but you could always wear a pair of gloves if you wanted. There are some shooting sports soaps that are designed to help really rip any lead off your hands, so you might use one of those if you're concerned.