If you delete the collections on the device and sync to Kobo, the collections will be deleted from the server. The next sync for the other device should remove them from there. If you let the driver delete empty collections, exactly what it does depends on the state of the collection. If it hasn't been synced, then it is simply deleted. If it has been synced, it is marked as deleted and the the next sync will finish this off.
If you don't want the books to sync from Kobo, you can go into the library on the Kobo site and move the books to the archive. Or, delete the books on the device and select the "more destructive" sounding option. I can't think exactly what it says, but it will remove the books from the device and move them to the archive. If you want the books back, you restore them from the archive. If you don't want to see them again, there is a delete in the archive.
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