Using Cafiine, no. Cafiine only allows access to the game's content, as in the content of the Smash Bros. disc.
(I think) replays in Smash Bros. are stored inside the game's save data. You can dump this save data from your console using Saviine, modify it and then inject it back into your console using Saviine again.
I don't, however, know how to actually modify the reply data. So unfortunately, no, it is not currently possible to use Smash Bros. replay features to upload videos. You'd probably get banned if you uploaded something that seemed impossible anyway.