Ammako It's not recommended to use Shizuku, as it requires ADB debugging and developer options to be enabled, which increase attack surface, and reduce the security of your device.
The recommended way of installing apps is via Google Play Store. All apps on GrapheneOS are sandboxed including Google Play Services. It doesn't really make sense to specifically avoid using Google products, and then install other services which compromise the security of your device. You can run Google Play Store and install apps in a separate user profile to the profile you actually use the apps, if you want to ensure that no usage information is communicated between your installed apps and Google Play Services via IPC.