We want to deploy our application on a cloud inside our corporate network so that it can be used to test APIs that exist within that network. We do not want to allow public access to this application nor to the internal APIs.
I've looked at deploying ICP internally onto resources (VMs) we've made available, but am wondering if IBM Cloud Dedicated is the better solution since I believe it's closer to IBM Cloud, which is where we've deployed our public-facing application.
IBM Cloud Dedicated is a single-tenant cloud environment, but it's hosted in an IBM data centre, so it might not meet your requirements. It can use VPN to securely connect to the local data centre - but that's also possible with public cloud, using the Secure Gateway. Depending on the sensitivity of the application, public cloud and secure gateway could be a good solution.
If you do want something inside the corporate nework, IBM Cloud Private (ICP) is a good choice. It's a significant part of IBM's hybrid cloud guidance so I personally wouldn't worry too much about technical differences between it and the public cloud.