I have a main connection string that I am using trough the application that uses SelfServicing. But what if I want to use another connection string for a specific query in a specific context (for example to connect to an historical database).

From what i checked in the documentation the only way to do this is to use the Adapter templates.

Is there a quick way to do this using the SelfServicing code?

Unfortunately we are still using version 3.5. Is there any advantage in this particular case upgrade to newer version?

You can change it globally, please check this doc page

Unlike the Adapter, where each call to the database is performed through an Adapter instance and you can set the connection string per instance.

This has not changed for SelfSericing in later versions. So if you want the Adapter behavior, you will need to migrate to the Adapter templateSet.