You should use the Adapter Scenario to generate your code.
This will generate 2 projects for you :
1- DBSpecific project
2- DBGeneric project
So basicly you should have the 2 databases identical (same names everywhere)
Then you would create a LLBLGen Pro project for each.
Note: coming soon, is a tool that you may use tol migrate an LLBLGen Pro project to another, rather than having to create it again, defining things like typed lists.
Use one of those DBGeneric generated (any one)
And use the DBSpecifc generated for each database.
Then you may usel either DBspecific project's DataAccessAdapter object to access the database. And pass the connection string to the DataAccessAdapter object's constructor.
Please refer to the following threads for further help:
http://www.llblgen.com/tinyforum/Messages.aspx?ThreadID=2095
http://www.llblgen.com/tinyforum/Messages.aspx?ThreadID=3080