I need to update a Oracle procedure via a .sql script
Just save the ddl for the procedure. This can be done using sql-developer 'save to file'. Tell the client to start sql-developer, connect to the schema where the code should be written and have them run the script using 'start' or the equivalent for start '@' script_name
The sql script should be located in the directory defined in the preferences for Database>Worksheet>'select default path to look for scripts'

@your_script


or

start your_script


It works from the worksheet, very similar to sql*plus.