How to change RDS instance type in Aurora cluster without downtime?

There is no way to change instance class of Aurora instances. It may take up to 15 mins. From this link : "Scaling isn't instantaneous. It can take 15 minutes or more to complete the change to a different DB instance class. We recommend that if use this approach to modify the DB instance class, you apply the change during the next scheduled maintenance window (rather than immediately) to avoid affecting users. "

OP, your strategy is mostly correct. Instances will become unavailable during the instance modification. With that in mind, you can upgrade your readers one at a time, or if you need at least two readers up at all times to handle load, add additional readers to the cluster in your target instance type and size. Once the readers are upgraded or added, you can fail the writer instance over to one of the upgraded readers. During the failover read and write operations fail with an exception. However, service is typically restored in less than 60 seconds, and often less than 30 seconds. You can improve this process with RDS Proxy. The proxy automatically routes traffic to a new database instance while preserving application connections. It also bypasses Domain Name System (DNS) caches to reduce failover times by up to 66% for Aurora Multi-AZ databases. Once you have three upgraded instances (one writer and two readers), you can delete any additional unnecessary instances. More information about high availability for Amazon Aurora is available in the User Guide.