Tenant to Tenant Migration from Existing Hybrid Model

The need for Exchange box on-premises is for staying in supported configuration, you can manage objects and attributes even without it just fine, you simply lose the "supportability" bit. Which seems to be the case for the other company anyway. Moreover, if you have migrated all mailboxes to ExO already, you can at least remove the Hybrid config, as you probably don't need it anymore. Regardless, you will have to make a decision on what the "end state" should be. Every configuration involving dirsync/AAD Connect "requires" the Exchange box.
If you want to manage objects centrally from AD, you will need the objects from the acquired company represented in AD. A more complex variation of the same theme is cross-forest migration, but since you plan to have all mailboxes in ExO anyway, that's an overkill. Probably the simplest solution is to do the migration to a single/consolidated tenant, either manually, leveraging the cross-tenant mailbox move functionality or via third-party tools, and ensuring there is a matching user object in your AD, so that you can continue managing them centrally.
Now, if you want mailboxes to be correctly represented on-premises, things get a bit more complicated, but judging from the above you have already opted to use the "simpler" model and are fine with it.