Here in Texas, I piddle around.
Piddle means something quite different here - you gave me quite the mental image!
To me "piddle" is a word the owner of a puppy or small dog would use to describe it urinating on the kitchen floor. "Aww did poopsie-whoopie do a piddle puddle?" or "Ralph get in the kitchen and clean up after this puppy! He piddled on the floor again!"
Yes. Puppies piddle. It's a bit cutesy for my vocab; but that is the meaning i know. I have also seen piddling used to demean something or someone ... piddling peasants, or a piddling amount (tiny amount) comes to mind.
The pi... word as discussed above, is used in Britain also in both the senses cited here by hobish.
Trivia item -- (I admit, getting further off-topic re puttering / pottering) -- in the county of Dorset in the south of England, there is a smallish river called the river Piddle, or Trent (not to be confused with the big river Trent further north). Said river runs through the villages of Piddletrenthide and Piddlehinton. Needless to say, all this provides much fodder for mildly off-colour humour, to kids of all ages...
The river also flows through a bunch of villages whose names feature not "Piddle," but "Puddle": Puddletown, Tolpuddle, Affpuddle, Briantspuddle, and Turners Puddle. Apparently there is a local tradition (suspected not to be true) that these places used to have "Piddle" names too, but were renamed to avoid embarrassment before a visit by Queen Victoria.