Why stir sourdough only with wooden spoons?
This is not true anymore, and modern recipes omit that part.

Back then, when silverware was made either from silver or pre-stainless-steel-alloys the acid in sourdough (and other foods*) would interact with the metal and corrode/color the metal and/or spoil the food.

So put your sourdough in your (stainless steel) mixing bowl and knead it in your kitchen machine as you like.


  *examples (thanks to @Stephie): eggs (there were special egg-spoons made from  horn or tortoise shell and later bakelite or plastic to
  prevent the sulphur in the eggs interacting with the metal),
  marmelade/jam (special spoons, jam would get runny if it got in
  contact with the wrong spoon), potatoes (there is a rule to not cut
  them with a knife).