I play Pokemon Emerald on the computer using VisualBoy Advance, so I can't evolve my Kadabra by trading it. Is there any other way I can turn my Kadabra into Alakazam?
You can't, for the exact reasons you stated.
While it would be possible if one of the ingame traders was willing to trade one, according to the Bulbapedia ingame trade list there is no such trader.
Apparently, there is at least one offshoot of Visual Boy Advance (though I've only located the one) which allows for emulation of the GBA Link Cable, and I'm assuming that running two instances of the program and connecting to
localhost would provide you with local trade functionality.
You have to get a certain emulator (I think it's a plug-in I'm not sure) called VBALink. You can find it here: http://www.vbalink.info/
You can then link up 2 running VGB emulators. You can also follow this video closely if you have any questions:
The first link basically allows you to virtually link up 2 gameboys together. The second link shows you how if you get stuck.
GameShark always helps, or if you trade. Otherwise, no you can't evolve it by yourself.