This. Just to expand on what you said a bit (since this is aimed at soldering newbies)...
The fumes from leaded solder don't themselves contain lead. The iron isn't hot enough to vaporize the metal itself. The fumes are from the flux, and breathing those can be problematic.
The immediate health risk in using leaded solder is all about touch and ingestion. Handling the solder gets lead on your fingers. That in and of itself is not a health risk unless you have a wound. But then if you touch food or mucous membranes (pick your nose, put your finger in your mouth, rub your eyes, etc.), you can get lead in your system. Not much, but once there, it doesn't leave, so accumulates over time.
You can mitigate those risks by wearing gloves, washing your hands immediately after you're done, and being rigorous about not eating or drinking at the bench and not touching other parts of your body. Non of that helps with the environmental problems of using lead, of course.