You can use the MCP2515 to generate a CAN frame. Here is the data sheet for the MCP2515
Datasheet
You will need to send the data to the MCP2515 by SPI, so you need an Arduino or something to generate the SPI signals.
Recently I helped with a project to generate CAN signals and we used
this and
this. All that was needed for the hardware was to plug one into the other. The driver library came from
here. The board that you found will do much the same as the Arduino CAN shield, but it doesn't plug into the Arduino so easily, and it doesn't have a 12 - 5 V converter built in. We didn't want to take time on the hardware so we used the more expensive option.
If you just want to generate CAN frames using a computer, something like
this will work fine and will take less setting up than an Arduino.
If you want minimal hardware, chose a mircocontroller with a CAN engine in it. That will need a CAN transceiver to get the voltage levels correct, and a board to fit it on, and something to program the microcontroller.