What is the safest way to install the sys schema on a production server?
Option 4: Download it from github and install it manually.

Installation would work like this:

# mysql -uroot -ppassword &lt; sys_56.sql


(I'm aware you're using MySQL 5.5. Please read on...)

When you examine what this does, you see that a separate schema is created and in this schema some procedures, functions, views and tables are created. Nothing too fancy. I can't imagine, that this would have any dramatic influence on the server.
Regarding compatibility with 5.5, I must admit that I'm not familiar with 5.5, but given that it's just some views and so on in a separate schema, I'd say that it either works or it doesn't. I personally wouldn't mind at all. Try it on a VM or docker container or whatever, if you like.