Agreed, neither works well.
Discussion
You could say you“own” or “control” #bitcoin whereas another person with bitcoin on an exchange like Coinbase does not own or control #bitcoin, but the nuance would be lost on a neutral listener
The dilemma stems from our current state of not being able to differentiate between cash and credit in modern #fiat world. Going back to a pre-#fiat world, the wording used would be “payable in specie” or similar specific wording
Bearer wallet. Still not perfect because it uses the word wallet, but it better defines the asset.
Bearer wallet—not bad. Not the best as you said but not the worst. Test drive it for a while, see how it goes
Then try en specie for entertaining conversations
Actually, call it like it is—you have keys. Keys to unlock the coins (transactions) on the blockchain. Time to let the wallet terminology go. Along these lines use keyrings, or time to bring back chatelaine