Drawing alchemical items to use faster

Exactly how could one be able to use alchemical weapons faster, without having to rely on a move action with a handy haversack?

rogue underground chemist can draw them as weapons at 2nd level

Be a Tiefling and get the prehensile tail racial trait. Let's you retrieve "small stowed objects on your person" as a swift action.

potentially a familiar. To an extent anyway. but that isn't the best.

Rapid Reload (Launching Crossbow)

A wrist sheath, spring loaded or otherwise.

So if you are a tiefling, it is actually better to retrieve a pot with your tail than with your hands?

Avr, can wrist sheathes carry potions/flasks?

Potions definitely, they're mentioned in the description. Flasks by extension of this but they're not specifically called out, I admit.