On a MacOS machine, is there any risk or trouble I'll encounter if I put some of my documents into a path that's not under my home ~ directory

I used to store all my files, documents under the ~ path.

I am wondering if I put my files out of my own directory, will there be any risk (like losing the files, or messing up my computer)

Yes, very much so. You break the convention that the files belonging to a user are located in his or her home directory.

If you „retire“ a user, only files and folders in their home directory are saved.

Catalina, for example, plainly forbids creating folders in the root directory (/).

To make a long story short: There are reasons for the home directory. Do not fight those. I for my part enjoy the peace of mind this gives me. And the fact that I do not have to search all over the OS. Let alone Time Machine Backups.