We typically print with Nazdar 9700 and let air dry.
You can heat press vinyl on faux leather, however depending on the grain the heat press will likely smooth out any texture.
If you want to go heat press route, just cut your backing very close to the image as it will leave indentation, or make it larger than your heat press bed, and use a lot of protection on top, since you'll get less heat go more time, and light pressure if you want the chance of keeping some of the texture if it is a textured material.