Yes you can delete the mechanical pump. There is a delete plate you can use off the shelf (for a Ford or Chev?) but making one out of an offcut of alu plate is easy. If the carb you're using has a return barb on it, that is straight forward to rig up but most Webers don't.

*The Mighty Mite fuel pump is capable of running a Weber carb so you're good to go on that.