This transmitter built by Walter Krämbring uses an Auriel transmitter card. Walter skips the op-amp entirely in his design and uses a single transistor to amplify the audio signal. To be perfectly honest, I am not sure that I understand how this connection actually works. I have a suspicion that is is dependent on the characteristics of the USB sound card he is using, so I recommend some experimenting with this circuit before you commit it to soldering.

The Circuit diagram is like this:

The transmitter device used is made by Auriel and called TX-SAW433/s-Z. It is available from many suppliers, but Walter recommends http://www.soselectronic.com, where the device costs 3.28 EUR.

Here is a closeup of the radio device and a USB sound card on the same board:

Walter has built in an USB sound card together with the transmitter, so the resulting device is a USB connected universal 433MHz transmitter. He uses the power from the USB-interface to drive the circuit. Here is the device with its enclosure. Note the connector of the antenna in the lid of the box.