There is currently no option to apply them in BizHawk, but you can still enter the equivalent cheat.
From http://bulbapedia.bulbagarden.net/wiki/GameShark :
Oh, and based on the example address given, the address given in the code is based on System Bus address instead of WRAM. So System Bus address C056 = WRAM address 0056, for example.
Just use this to determine what value should be written at which address, and enter the cheat directly.
There was another topic on this forum about it as well: http://tasvideos.org/forum/viewtopic.php?t=13991
FractalFusion is correct.
Whilst this doesn't pertain to your question directly, I thought I'd quickly add that it's the same deal for N64 Gameshark codes. The following code for instance, 802808DF 0000, would be activated by setting a value of 0000 in the address 2808DF in the RDRAM.
I'm not as active as I once was, but I can be reached here if I should be needed.