If you take a look at the deployJava.js script and the runApplet function is says:
/**
* Ensures that an appropriate JRE is installed and then runs an applet.
* minimumVersion is of the form #[.#[.#[_#]]], and is the minimum
* JRE version necessary to run this applet. minimumVersion is optional,
* defaulting to the value "1.1" (which matches any JRE).
* If an equal or greater JRE is detected, runApplet() will call
* writeAppletTag(attributes, parameters) to output the applet tag,
* otherwise it will call installJRE(minimumVersion + '+').
So if you make the call like this
deployJava.runApplet(attributes, parameters, null);
or like this
deployJava.runApplet(attributes, parameters, 'undefined');
or like this
deployJava.runApplet(attributes, parameters, '1.1');
it will only check if Java is installed at all, and only then redirect to java.com for installation. And since you have an applet, you do need Java :)
Alternatively you can call deployJava.writeAppletTag(attributes, parameters) directy:
/**
* Outputs an applet tag with the specified attributes and parameters, where
* both attributes and parameters are associative arrays. Each key/value
* pair in attributes becomes an attribute of the applet tag itself, while
* key/value pairs in parameters become <PARAM> tags. No version checking
* or other special behaviors are performed; the tag is simply written to
* the page using document.writeln().
*
* As document.writeln() is generally only safe to use while the page is
* being rendered, you should never call this function after the page
* has been completed.
*/