I cast a lot of bullets from lead alloys. I take a lot of precautions to avoid breathing lead fumes. However, just handling lead is usually not going to contaminate anything.
Wash carefully with a good strong soap with running water, warm by preference. Then dry your hands with a towel. Put the towel in the laundry afterwards.
While handling the lead, avoid touching your face, especially around your mouth and eyes.
I tried some of the larger weights that had an eye cast into them. I put yarn streamers about 4 inches long (10cm) in the eye. And when I threw them, I didn't recover a single one, they buried past the yarn.
The yarn did make it easier to track them by eye, though.