MySql: Change from latin1 to utf8
Setting the default character set and collation is completely safe. This will ensure that future DDL changes will use utf8, but will not affect existing columns that use latin1. Those will have to be converted to utf8. Make a backup of the data, because there are risks of data corruption (one example).

And for completeness, I will point out that adding the changes in the my.cnf will require a server restart.