I currently have a Postgresql v9.3.3 running on AWS RDS. I've learned that if I upgrade Postgres to 9.3.5 that I can create read replicas.
However, I am afraid of losing data. Can I just select "modify" from the console "instance actions" section and upgrade to 9.3.5 without losing any data; or do I need to do something special?
You're fine - if there is a possible data loss AWS wouldn't provide a single click update. As this is only a minor version update it is pretty easy to upgrade without any problems.
What Osterjour said is only partly true. There is almost no way to lose data, especially if configured in multi-az.
To avoid losing data you would have to come up with a data integrity validation strategy prior to upgrade and post upgrade even if is minor upgrade.
From experience= i migrated postgreSQL 9.6.6 to 9.6.9 (minor upgrade). Small validation and the downtime was 12 minutes due to manual snapshot and automatic pre-upgrade and post-upgrade performed by AWS RDS. In general terms it was good and everything was smooth.
Recommendation= test. Do dry-runs many. and pay attention to the DB load plus the DB extensions.
Check AWS official Doc. AWS RDS Upgrades
Please Let us know after 4 years what you decided and how did it go?