Well, they do offer http://us.battle.net/support/en/article/battlenet-sms-protec... which provides an extra (but different) layer of security.

Assuming you're from one of the "supported countries", though, which aren't listed.

Run java?

http://arenabooster.marisil.org/bma.htm

Nope:

    The Java-based (J2ME) versions of the Battle.net Mobile Authenticator previously
    available through this website have been discontinued.

http://eu.blizzard.com/en-gb/mobile/

Find an apk and toss it on an Android emulator?