How do I recursively run "chgrp" without changing the group if it matches a specific group?

I just copied all the files/subdirectories in my home directory to another user's home directory. Then I did a recursive chown on his home directory, so that he became the owner of all his files/subdirectories. The last thing I need to do is a recursive chgrp on his home directory, so that his username will be the group for all his files/subdirectories, instead of my username. The issue is that there are a couple of subdirectories whose group is "docker". Inside these subdirectories, there are some files/directories whose group is my username, and some other files/directories whose group is "docker". How do I recursively run chgrp on his home directory so that every single file/subdirectory whose group is my username gets changed to his username, but every single file/subdirectory whose group is "docker" stays "docker"?