Since you always carry it around with you you should just be able to go right into parrying with it right?
Thinking about using one of those for the parry trait and RP on a wizard and later pick up fighter dedication for proficiency with the other half.
Sounds reasonable enough
You’re usually carrying it around by the top so it’s not really in position for a parry.
That depends - if you are in formal society you most likely hold it at the knob at the top - which is not a good point to parry, I agree
If you are on the move, especially if you have to move fast you are probably gripping it below the knob on what is the sheath - and while it might not be as comfortable as holding the sheath the other way around you can certainly use a backhand grip to block an incoming strike
You’re usually carrying it around by the top so it’s not really in position for a parry.
I would consider that readying a parry is like raising a shield, getting something you're already carrying in your hand in position.
It doesn't take more than 2 seconds to move a stick from an overhand grip to a forehand grip imo.
Maybe, but switching grip on a weapon is a single action in PF2, which is enough of a action economy cost that I wouldn't let you do it for free.
This lists how many hands it takes to use the item effectively. Most items that require two hands can be carried in only one hand, but you must spend an Interact action to change your grip in order to use the item. The GM may determine that an item is too big to carry in one hand (or even two hands, for particularly large items).
You could walk around ready to parry, but everyone would see you wielding your swordcane sheath like a weapon.