You will need to have at least one domain that is added to both EXO and Exchange on-premises, that is called a "Hybrid Domain" and that needs to be in place.
Running the HCW in minimal configuration mode will not change the way your mail is routed since there are no connectors created.
We do not publish all of the changes that we do with the HCW, but essentially we add/modify accepted domains, remote domains, Email Address Policies, Web Services Virtual Directories, and tenant settings like DirSync enablement and Tenant Hydration.
We log all cmdlets we run in the HCW log so you can review the changes we have made there.
Not knowing all the detail of the scenario I cannot say for sure, but it sounds like a good candidate for doing the minimal Hybrid configuration. If you want the steps to remove hybrid please consult this document: https://technet.microsoft.com/en-us/library/dn931280(v=exchg.150).aspx