Unfortunately, it seems that both replays and photos are in novel formats. Also, you can only send things to friends with Brawl. Since you can pause the replays and move the camera around it won't be a video, more a list of who did what.
The directory structure looks a bit like this (where / is the root of the SD card):
/private/wii/app/RSBJ/al/al_080202_2040.bin
/private/wii/app/RSBJ/rp/rp_080202_1725.bin
/private/wii/app/RSBJ/rp/rp_080202_2039.bin
Where al is photos (album), and rp is replay. 080202 is the date in YYMMDD. I'm not sure what the second number is, since it doesn't match the time displayed.
Note that both videos are exactly 1024 bytes (different number of characters, both stock so different time lengths), and the photo is 99456 bytes. This makes me wonder about the photos being like the videos, a description of who is where, and makes me wonder if they're actually some kind of image. If it is an image, then it should be possible to convert it to a normal format somehow.