You will unlock the Parasol Gun later in the game (sequence 3-3) which functions as a blowpipe for the Lady Persona.
However I was only able to hold 5 poison darts and I thought the darts were really expensive. But I found that the poison darts get restocked if you just switch Persona (I used Lady to Assassin and back). So that is a quick and cheap way to have enough poison darts for this to work.
If you are far enough in the game, and you have enough money. Make sure to buy the upgrade for the holder so it can hold up to 20 darts