I do not believe that "lead fume" exposure in recreational electronics soldering is a problem. Lead has to get a lot hotter to make much Lead vapor. The pool of hot lead is small and quickly cooled. If you are soldering right, 2 seconds of just-barely above the melting-point, then re-set to do the next joint.
That NIH report does not mention solderING, but "sources of exposure... paint, industrial processes, water contaminated by corroding pipes or solder, mining, pottery, and folk medicine."
Hand-washing is an excellent thing. Skin is not so good at absorbing metals, but then you need a snack (or a smoke!) and anything on your skin gets inside you.
Note that my attitude is corrupted by a childhood snorting lead from car tailpipes. If you are so young that you have never seen leaded gasoline, have never drunk from soldered pipes (home school or work), then you may wish to be more careful than I.
If you solder for hours at work, make your boss buy a fan.
If you work with solder-dip, a vat of molten solder, lead fumes can be substantial and you should observe ALL safety rules and report all fume-hood problem.
The "fumes" in soldering are mostly the flux. Electronic soldering flux is usually Rosin. Rosin is pine-tree sap. I live in the Pine Tree State and I say pines are your friends. Most people (~~95+%) get only minor irritation from casual rosin fumes. However like any complex bio-chemistry, some people have unusually strong reaction, and must switch to needlepoint or motorcross, something that does not involve rosin fumes.