How can I generate an Amazon affiliates link (with my Tracking ID) from a regular link without using Amazon online tools ?
While I don't have an answer, a good start would be to compare the elements of the affiliate link from the tracking tool to the identifiers on the item page.
From what I recall every Amazon product has a unique identifier (ISBN for books) and this identifier, along with your tracking ID, is stored in the affiliate links.
It should be rather straightforward to reverse engineer the format.