RF link wireless trigger (press/hold) with no mcu
Depending on exactly what information you need to send to the card (e.g. simple pulse, or a few bytes, or..) you could do this a few ways.    

If you have one lying around, hacking a wireless alarm doorbell / garage opener or similar might be an easy option. Press, release and hold may not be part of the standard setup though.    

The tx/rx eBay modules you mention should be fine for this, you can also get wireless relay/switching kits that are designed for this type of simple application (e.g. press button, toggle switch or logic output) Some have a transparent mode where they just send exactly what is input, so a switch and flip-flop might do what you are asking for.  

If it's line of sight and you can lower the distance requirement a bit, an IR (infra-red) tx/rx might be the way to go.  

If you give a few more details on exactly what you want to send (e.g. does the switch have to latch, or just do exactly what the button at the transmitting side does?), a more specific answer can be given.