Hi,
You are correct, the webpmux binary has no flag for changing the dispose method of an already animated WebP file.
I suggest uncompressing your WebP animation to one PNG per frame using the anim_dump binary, and then using webpmux with the -frame +[ms]+0+0+[dispose] flag to set the dispose method to 0 or 1 for each frame.
Unless your WebP animation was compressed without loss (cwebp -lossless), I strongly recommend starting from the original files used to generate your first animation instead of recompressing it. It will avoid forwarding compression artifacts.