Why .177?
Just wondered if it may not have been driven by available tube sizes as speculated in my last post. Could it be that an airgun developer would have popped down to his local shooting supply shop or hardware store & bought a big bag of shotgun reloading shot or popped round to a shot maker & asked what he'd got in the way of lead balls that gave a nice number for weighing out into smaller packs, say around 50 to the oz? With a view to selling ammunition for a new airgun he was developing & thinking about the supply of ammunition for it if it took off & the market opened up.
Looking around the turn of the century (1900 ish) although shot designation seems not to be too standard at all, for instance there are differences between French, Belgian, USA & Britain. Even within Britain there were differences between them AS or 2A shot from Walker Parker, gave 40 per oz new chilled Newcastle AA shot gave 48 per oz. So manufactures method, production variability, lead alloy or pure, would have given a variety let alone anything else so conceivably with the right conditions etc 50 balls per oz could come close to 4.5mm & perhaps suit the purpose of our developer. Just an idea, not sure if it's a good one or not but maybe something to contemplate...