If you use Bitcoin-QT (or any wallet client, including some web ones, that allow you to import private keys using just the priate key) you should be able to import the wallet, send money out, and then remove that address from your wallet once again.
It'd be up to you to be sure that you deleted any trace within your memory or hard drive of that private key. But if you could do that with certainty you should be able to 'import' your paper wallet momentarily, send BTC out to another of your addresses (or to someone who is expecting payment) and then delete it again. All without having to update all your backups.
Similarly you can, as you stated, just send money to that public address of your paper wallet's whenever you want to store some more there.
Blockchain.info's wallet lets you "import" paper wallets without sending the money out of that address (it asks if you want to "sweep" the wallet, and even recommends it but you can say no and it will just bring in the wallet address -- however I don't know of a way to 'delete' that address from your account's record after that on blockchain.info).