Copying millions of rows to a new table

I have a mysql table that has 100+ million rows and we need to add a new column to this table.

TABLE

will lock the table and I can't have that, so my next idea was to make a new table that has the new field and then just move the contents over using a script of some kind. however, I wanted to see if I had some other (possibly better/faster) options available to me. The MySQL database is an RDS on AWS (So it's an Aurora Database that's MySQL-flavored), so if someone know of some AWS magic, I'm all ears. There's not that many indexes or any relationship setup (this system is a legacy system that never had a DBA design things). I have considered using mysqldump to extract the data, but wasn't sure if this is a worthwhile route to go. Any suggestions/ideas would be appreciated.