How do I evolve Kadabra to its final form without trading it?

Solution 1:

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.

Source: Bulbapedia

Solution 2:

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.

Solution 3:

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.