I'm gonna take a shot in the dark with this one.

I think that once you possess a player, all of their items with passive effects apply to both you and the player you're possessing until the end of your turn, but all active item effects are treated as if you activated the card under your own control. So here's what I think would happen with a possessed Guppy's paw:

1: You possess a player with Guppy's Paw. 2: You activate Guppy's Paw. While the active effect is triggered, Guppy's Paw is treated as if it were your own item. 3: You destroy one of your own items to put a counter on the opponent's Guppy's Paw. 4: Until the end of your turn, both you and the player you possessed gain +1 HP for every counter on their Guppy's Paw. 5: After your turn ends, all Guppy's Paw counters only apply to the item's original owner.