You can delete logs if you don't need them. They are only useful for debugging stream issues, and if your stream is running fine, there's no use in keeping them around.
To answer your question, you can make that folder symbolically linked to a folder on your hard drive. First, make sure OBS is closed. Then copy the %appdata%\OBS folder to a different hard drive, and then delete the version in %appdata%. After that, run a command prompt as an administrator, navigate to %appdata%, and run the command
mklink /d OBS X:\path\to\copied\folder\OBS
Where X is your other hard drive letter.
What that should do is make a symbolically-linked folder in %appdata% called OBS, just as OBS expects to be there, but when you navigate to it, you end up on the other hard drive.