Bismuth? Low enough in melting point to do some mucking around on in the shop. Most the density of lead, not much of the toxicity.
Bismuth is a rather odd element to include. It is rather expensive and somewhat radioactive. It is questionable if it is less toxic than lead - mainly less common. So I see no practical use at all.
The main alternative heavy element is tungsten, though a bit hard to machine and also not cheap.
Lead has the desity advantage and in addition, especially for the lower energies also a higher effect per mass. For some 100 keV 1 kg of lead may repalce some 5 kg of iron.
Also at high energies there is also a slight advantage per mass, though not that much.
Compared to rock and concrete the background of lead is relative good. For shielding a detector / sensitive experiment the radioactive contamination in the shield also becomes a factor. So contrete is limited.
The background radiation is a mix of both high and low energies. The lower engergies come from more local radioactivity and also conversions of cosmic radiation (e.g. myons or pair generation from high energy gamma). It depends how relevant the energies are - some detectors can discriminate in the energy and thus largely ignore parts of the background.