> practically keep in sync on a battery constrained device

Simply don't, and have it be an app for blockchain.info (ie, someone else hosts the wallet and sends the money) or for your own personal wallet (that you have hosted somewhere).

But in practice, all you need to initiate a bitcoin transaction is the signing key of your address and someone to send your transaction to in the swarm. You never need the blockchain itself to do anything - if you forge illegal transactions where you say "give 50 bitcoin to X, but I only have 5" the chain will disregard it as false. You don't have to know your own balance to do that. And you don't need the blockchain to know your own balance - plenty of web services provide APIs to query the balance in a wallet.

And common retail works just fine here. The store is an entry point into the blockchain, and it is in their interest to provide a valid entry point to submit transactions through. They can't modify your transaction because they don't have your private signing key to authorize it, but if they don't broadcast it and have it confirmed in the swarm they can't get paid. It doesn't get quite as simple as "swipe a card" because you need some transistors that construct a valid transaction that requires your private signing key, thus you can't use a public terminal to generate it. But it doesn't need to be complex, have internet access, or have a complete blockchain to work.