Moving fluid with minimal shearing requires a positive-displacement (PD) pump. PD pumps can move fluid with a minimum of shear because the product is moved, in the case of a rotary PD pump, within the rotor pockets from the inlet to the outlet.
Popular PD pumps for low-shear applications include rotary types such as peristaltic, lobe, and eccentric disk pumps. In addition, diaphragm pumps belong to the reciprocating family, but like the three rotary types, are able to move product safely without shear.
The rotary lobe pump will probably be the least expensive.
i would keep the pump operating continuously; otherwise the solids will settle out and foul the piping.