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.
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.
I don't personally use lead solder for this reason. If you have a good temperature-controlled iron then SAC305 is almost as easy to use.
[1] https://en.wikipedia.org/wiki/Restriction_of_Hazardous_Subst...
It's horrid to use. And the lead-free stuff is far worse in manufactured equipment - how many devices have failed early due to BGA solder joint failures that basically didn't exist before RoHS requirements? I think the nVidia 8600M issues were traced to that, and plenty of other BGA equipment since 2006 or so has failed rather early.
I use Chipquik SAC305 with water-washable no-clean flux core and I actually prefer working with it over Sn63Pb37.
My lead-free joints come out nicely rounded and shiny just like my leaded ones with some practice and the right consumables. But I certainly have to break out hot air station more than I would when using leaded solder to deal with larger thermal masses (and why I will still break out my spool of leaded wire on rare occasion when I'm working with temp-sensitive components and just want it on the freaking board).
This is why hobbyists are often still using leaded solder, particularly outside of the EU. But also in the EU, because it just flows so damned nice.
I find SAC305 to wick into joints faster than leaded solder does, provided you have quality flux in the solder.
If you get the cheapest lead-free solder you can find on Amazon it will be bad.
Doubly so if you have a non-temperature-controlled soldering iron. Too cold, and it won't melt effectively. Too hot, and exposed metal will oxidize rapidly.
Works beautifully with SAC305.
which you often don't need with leaded solder.