Well, based on the screencap from “The High Ground” that Ethan posted with it sitting right next to a standard Hypospray, we’ve determined it’s the same length. Width-wise, I’d say it’s the same diameter as the ribbed neck beneath the spray head.
If we want to get more precise, from my observations of that particular screencap I’d say the back end half is the same length as the gray grip on the Hypospray, with the recepticle for the vial and the (likely machined brass) tip evenly split to make up the other half.
That’d be my guess, anyway
EDIT: The production-made Hypospray casting I got from Mike a while back measures 5 3/8" long (minus medicinal vial) with the ribbed neck having a diameter of 1", if that helps.