I’ve been looking mainly at Mifare Classics (MFC) for my thesis.
Most cards are identified by their ATQA and SAK values, however there is no difference between a 1k and a 4k in terms of those values. This is usually why they can be positivly identified as a MFC but can’t really suggest if its a 1k or 4k. Best way to tell would be to try to read sector 31 (last sector on a 4k). You could also scan it with NXP Tag Info, this should give you the chip type.
Depending on what sectors are being used, you might be able to use a 1k. From experience, most readers can’t tell the difference between a 1k or 4k card unless they use a sector >15 (ie only on a 4K).
If you can identify the reader, the datasheet may mention if it has clone detection. Usually this is done by sending a backdoor wakeup command to the card, if it replies then the reader stops communicating. Reason why Gen2 cards are generally recommend to ‘bypass’ this detection.
Best idea would be to to get a 1k Gen1a magic card and clone your tag to it. However, you will need something like the Proxmark3 to utilise those backdoor commands. Once successfully cloned, present it to a reader. If the reader doesn’t process the tag it could have ‘clone detection’ or have an issue with it being a 4k. (I know there has been some issues with this already)