You don't want to eat and drink from lead (or uranium) platters and goblets every day for years, but doing it once hurts you less than breathing in in any densely populated city.
If you do not have open wounds or sores, handling heavy metals like lead or mercury is safe. Just wash your hands afterwards, so you do not end up ingesting them.
(If you do have wounds or sores, it depends on the material structure. Usually it does not matter. The risk, really, is getting some lodged in the wound, so your immune system tries to slowly digest it. You wouldn't want to deal with heavy metal powders with your bare hands, if you have cuts in your hands. Just use gloves then.)
Welding and soldering generates fumes. Welding generates metal vapor (zinc vapor being particularly nasty) and small metal particulates, and both welding and soldering vaporizes some of the flux. These are most chemically active when hot, so you don't want to breath them in fresh. If the small particulates are still hot when they get in your lungs, they can embed themselves in the tissues, and since there is a lot of blood flow there, it is not far off from getting them directly in your bloodstream. So that's bad. Venting the fumes cools them down, making them much, much less chemically active and thus much less dangerous, and mixing them to the ambient outside air reduces their density to safe levels. The fumes are much more dangerous in closed spaces: that's why you should always weld outside or a special room with fume extraction and/or air filtration.
If say a factory or a hack lab has welding or soldering stations, they should have an air filter unit. However, this too is a balance: making such air filters takes resources and generates pollution, so such an air filter really should be used enough to warrant itself, or it will be a net loss for the environment.
Environmental risk management is something where you need both rational thinking, and a wide range of facts to rely on. (For example, like 238U being a heavy metal and dangerous due to its chemistry, like lead and mercury, and not because it is radioactive.)
It truly is pity that leaded solder is considered dangerous, as the amounts used are minuscule compared to other industries, and the way they are used means the lead is in environmentally pretty safe alloys. The chemically harsher fluxes needed with non-leaded solders probably negates any benefits anyway.
Anyway, the small bit of 60/40 solder I just ate, didn't taste of anything. Explains why the Romans used lead in their dinnerware. Stainless steel has much more of a "metallic" taste. If I get sick, it would be because of the flux in it. I won't, though.