This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
An obsolete Java version and crypto library running as part of an obsolete Java mobile API via a hack on an obsolete mobile OS - tall order . I have added this post to the Java ME forum as well.
My starting approach might be to determine which ciphers are supported by the server (using a tool like SSLScan), and then read through the JSSE 1.0 documentation to see which ciphers that supports - thereby determining whether there is any overlap.