A fluid pump comprising a piston chamber-forming member defining a dispensing chamber therein with an inner end and an open outer end, the inner end having a fluid inlet to be placed in fluid communication with a source of fluid (12, 16) being a reservoir comprising a chamber, a piston-forming element received in the dispensing chamber of the piston chamber-forming member axially slidable inwardly and outwardly therein, the piston-forming element having an axially extending hollow stem which extends out of the open outer end of the piston chamber-forming member, the stem having a central internal passageway ending at a discharge outlet, the piston-forming element cooperating with the piston chamber- forming member whereby in a stroke of inward and outward reciprocal sliding of the piston-forming element in the dispensing chamber of the piston chamber-forming member between a retracted position and an extended position, the piston-forming element pumps fluid from the source of fluid (12, 16) from the inner end through the piston chamber-forming member via the passageway in the stem and out the discharge outlet, an engagement mechanism on the piston-forming element adapted for coupling to an actuator catch member for sliding of the piston-forming element relative the piston chamber-forming member, the engagement mechanism extending radially outwardly from the stem outwardly of the open outer end of the dispensing chamber characterized by: the engagement mechanism comprising a plurality of resilient finger members extending radially outwardly from the stem in an unbiased inherent position spaced circumferentially about the stem, the resilient finger members each being resiliently deflectable radially from an unbiased inherent position to a deflected position of a different radial extent than the unbiased inherent position upon coupling with the actuator catch member and biased to return to the unbiased inherent position when deflected away from the unbiased inherent position toward the deflected position in a coupled orientation, each resilient finger member including a radially distal end deflectable away from the unbiased inherent position toward the deflected position to biased positions with the radially distal end resiliently deformable from the unbiased inherent position to the biased positions. the engagement mechanism comprising a plurality of resilient finger members extending radially outwardly from the stem in an unbiased inherent position spaced circumferentially about the stem, the resilient finger members each being resiliently deflectable radially from an unbiased inherent position to a deflected position of a different radial extent than the unbiased inherent position upon coupling with the actuator catch member and biased to return to the unbiased inherent position when deflected away from the unbiased inherent position toward the deflected position in a coupled orientation, each resilient finger member including a radially distal end deflectable away from the unbiased inherent position toward the deflected position to biased positions with the radially distal end resiliently deformable from the unbiased inherent position to the biased positions.