If the distribution of your game is limited and there's no real money/bounty involved for the players to win, your original scheme is probably enough.
Using SWF Encrypt will likely make it a little bit more difficult to extract the key, and it could be a good tool to use even in a more advanced system as well. But if you have a real public/private key scheme (e.g. RSA), it's really a moot point since the public key isn't a secret, it's not supposed to be. Still to prevent most people from editing the code and tamper with the scoring system, SWF Encrypt is probably a good enough choice.
Just to make you a bit more paranoid I wrote the following as well:
The problem with SWF Encrypt, as with most other similar tools, is that it must still be possible to execute the script on a (possibly compromised) machine. So all information must be available on said machine. Compare that with a classic use of cryptography, sending messages:
When you send an encrypted message, you typically trust the source and the destination, so both of these have the key to decrypt the message. What you don't trust is the courier, or at least not that your enemies will not intercept the courier. So the courier does not have they key and your message is safe.
Your problem is instead that in your case you trust the destination (you) but not the source (the client) or vice versa. Still you need the source to be able to encrypt the message since you trust the courier even less. So the source needs to have all information to encrypt and decrypt messages in order to function. Your problem is that you cannot see the difference between a "good" source and a "bad" source.
What I mean is that since the code must still be possible to run on a client, the information to do so must be fully available, albeit possibly in obscured form. A hacker could for instance create her own ActionScript compiler that transform the obfuscated ActionScript code into something readable and make appropriate changes. Difficult but definitely doable.
Yet this level of sophisticated attacks will most likely not be a problem for you, if you have a limited distribution and no real bounty to win.