I think we would need vastly higher speeds than that.
See the Wiki article:
http://en.wikipedia.org/wiki/Redshift
Scroll down to
Redshift formulas, about 1/5 of the way down the page. Your number matches the one in the animation on the right. The math itself is not wrong, but it appears to be applied to the wrong type of light source. We might get that much color change with a monochromatic source such as a low pressure sodium lamp, because our eyes are extremely sensitive to slight changes in the wavelength in that range. However, that is not what we have in an incandescent object such as a star. Here we have a broad spectrum whose maximum amplitude is at a wavelength inversely proportional to the temperature. The color is very pale compared to that of a monochromatic emitter, and a much larger redshift or blueshift is required to cause a noticeable change. For small shifts such as the Wiki sample, the color change from shifting any given component of the spectrum will be washed out by the concurrent changes of adjoining components.
Sirius has an effective temperature of about 10,000K. To make it look like an M type star (pastel orange) we need to redshift the the wavelengths of the broad spectrum by about a factor of 3 to match the M star's effective temperature about 3,300K. From the formulas given in the Wiki article, I find a velocity of about 0.8c, or 240,000 km/s, away from us.
To make Sirius look like an O or early B star (very pale blue), we need the spectrum corresponding to about 30,000K, which means shortening the wavelengths by about a factor of 3. This requires about 0.8c toward us.
The relative velocity of Sirius has had no major change in recorded history, and even if it did, it is too slow to have any visible effect on the perceived color.