So when you say "API versions" are you actually talking about the Adobe Analytics API, such as:
https://github.com/AdobeDocs/analytics-1.4-apis
or
https://github.com/AdobeDocs/analytics-2.0-apis
If so, I believe the older 1.4 version has that coded into the request (something like https://api.omniture.com/admin/1.4/rest/?method=Report.Get)
I think the request url of 2.0 used to have 2.0 in it, but I don't know if it does anymore.... but since there are only 2 working API versions at this time, by looking at the request, you should be able to determine which is which.
If this is not what you are referring to, since the I don't know why you would be calling the API with Adobe Launch, are you perhaps referring to the version of your Launch extensions?