I'm going to go out on a limb and elevate my previous comment to an Answer. Without root access, and without breaking the default security of the AIX system (by opening the password file up to non-root users), non-root users cannot read the encrypted password file, therefore non-root users would not be able to compare any password to the existing one.
The best option I can imagine is to attempt a login with the account and assumed password, then check the results. If you're running locally to the system, you could telnet or ssh to localhost; if you're remote, you'd be limited to whatever external login methods are running (e.g. ssh). Wrap the login process with perl or expect and see if it worked. (If you cannot install such tools on the AIX system itself, then use or install them from a remote system). One minor down-side to this approach is that if your password is not correct, it would increase the failed login attempt by one for that user. Doing so probably will not cause a lockout of the account, but it's something to be aware of.