I would not recommend destaining the gel because most destaining protocols use methanol and that would fix the protein. Although I have not tried this myself, my guess is that the protein should be still active even with the Coomassie blue. The other option is to exchange the Coomassie blue containing running buffer with colourless running buffer after about a third of the run is done, as that would remove most of the coomassie blue from the gel.

Thanks a lot