A glassware forming machine blowhead arm assembly includes a one-piece blowhead arm body having at least one longitudinal air passage and a plurality of lateral air passages connected to the longitudinal passage. A blowhead chuck is removably received in a first end of each lateral passage and a cap is threaded into the second end of each lateral passage spaced from the associated blowhead chuck. A spring is captured in compression between each cap and an associated blowhead chuck biasing the blowhead chuck in a direction out of the lateral passage and away from the cap. In an exemplary embodiment of the disclosure adapted for use in conjunction with so-called isolated finish cooling blowheads, there are first and second longitudinal air passages extending through the blowhead arm body separately from each other, and separate air inputs in the body respectively coupled to the first and second longitudinal passages. Each lateral air passage is separately connected to the longitudinal air passages, and the blowhead chucks have separate air passages for feeding blow air and finish cooling air to a blowhead mounted in the chuck.