Classification works with data that have already been tracked. So that won't work for you since your order IDs are not tracked at all.
You can consider the Bulk Data Insertion API https://developer.adobe.com/analytics-apis/docs/2.0/guides/endpoints/bulk-data-insertion/ . However, that requires that you have your visitors' visitor ID values (usually the Experience Cloud IDs), so that AA can associate your imported data with the correct visitor data that has already been collected. If you don't have that, you can still import your orders data with dummy visitor IDs, but obviously that means you won't be able to take advantage of any attribution reporting, e.g. reporting the orders per Marketing Channel.
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... or... you can sweep this under the rug and wait for 2 years for Adobe Analytics to delete old data automatically and have your problem "vanish" with that... yes, that is not a real recommendation, please don't use it!
