Though Dataproc doesn't currently provide a direct option for using static IP addresses, you can use the underlying Compute Engine interfaces to add a static IP address to your master node, possibly removing the previous "ephemeral IP address".
That said, if you're accessing your UIs through external IP addresses, that presumably means you also had to manage your firewall rules to carefully limit the inbound IP ranges. Depending on what UIs you're using, if they're not using HTTPS/SSL then that's still not ideal even if you have firewall rules limiting access from other external sources.
The recommended way to access your Dataproc UIs is through SSH tunnels; you can even add the gcloud compute ssh
and browser-launching commands to a shell script for convenience if you don't want to re-type all the SSH flags each time. This approach would also ensure that links work in pages like the YARN ResourceManager, since those will be using GCE internal hostnames which your external IP address would not work for.