From what I am compiling from RFC 5280, key usage extensions can only decide whether a certificate can be used to sign a code or not. In the RFC, there seems to be nothing to limit whether you are signing Java or AIR code or something else. This seems to mean that if you can sign one piece of code (or any other kind of non-key data), you can sign it.
However, there may be CA-specific extensions in your certificate. Without seeing the certificate, it is difficult to say if there are restrictions.
From a technical point of view, as long as the client (i.e. the browser, if we are talking about applets) recognizes the CA and is satisfied with your combination of using the key and certificate type (DIGITAL_SIGNATURE and OBJECT_SIGNING), then you should be fine.
Cameron skinner
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