Your option #1 sounds like a "fork lift". That is a term used in Teradata Professional Services (PS) to describe a quick move off an old platform and on to a Teradata platform. This is not uncommon. The data model of the old system is ported to Teradata and then the data is transferred. This is quick but not ideal. This will not leverage the full value of the Teradata platform. The data model design, (LDM/PDM) , should be adjusted to leverage Teradata database strengths. A subsequent move to a Teradata specific data model on the same Teradata platform may be what you refer to as mapping.
Your option #2 sounds like a new model on the Teradata platform being filled from the old database. This would be the preferred approach. This will get you the most bang for your buck from the Teradata platform. It may not get the data accessable on the Teradata platform as quickly as your option #1. Even with option #2 it is likely you will make a staging area on Teradata so you can use an ELT process rather than an ETL process.
In either case, the mapping from the old data model to the new will take the same amount of time. Teradata has a tool to assist in the mapping. It is Teradata Mapping Manager. It works with your modeling tool to speed up the modeling task.