This can be done simply using Pywal templates

1. Just move your cava config to ~/.config/wal/templates/cava_config , and then replace the colors with {color0}, {color1},... etc.

mv ~/.config/cava/config ~/.config/wal/templates/cava_config

Recommend colors :

[color]
gradient = 1
gradient_count = 4
gradient_color_1 = '{color1}'
gradient_color_2 = '{color2}'
gradient_color_3 = '{color4}'
gradient_color_4 = '{color5}'
gradient_color_5 = '{color6}'

2. Then after you run pywal, just link your cava_config to cava/config back from ~/.cache/wal/

ln -s ~/.cache/wal/cava_config ~/.config/cava/config

And you are done.

Reference: Github Issue | Pywal template docs