The game mentions that shields are weak to electric damage. Does this apply to full-body shields carried by Nomads and mini-bosses like Doc Mercy/Bad Maw?
No. The specific weakness to electricity only applies to energy shields worn by enemies, which are the equivalent of the energy shields worn/equipped by players. Enemies with energy shields weak to electricity will have a blue bar above their health, as seen in image B below.
Image A denotes a physical shield worn by a Nomad (not weak to electricity). See this post to deal with them.
Image B denotes an energy shield equipped by Master Gee (weak to electricity).