Is there a simple, safe and low cost way to implement a (limited) database to be outside (close) IT control?
Here's my view of the situation:

The data you are working with already have a source; they are extracted from some data mart or "system of record" and given to you, probably as a CSV file or something, which you load into Excel and build your models. Subsequently, there is already a database that has the data you need. Further, there is probably a bunch of development and QA (that is, non-production) versions of this database, to which it is much easier to get access. 

If that is so, your best chance would be to discover where your data are coming from (if you don't already know) and ask your IT to give you access to a development copy of that database. Since they already maintain it, there won't be much extra effort required on their side and they might be less reluctant to help you.