I'd have thought your approach seems reasonable, but reducing an entire image to 1x1 pixel in size is probably a step too far.
However, if you converted each image to the same size and then computed the average colour in each 16x16 (or 32x32, 64x64, etc. depending on how much processing time/power you wish to use) cell you should be able to form some kind of sensible(-ish) comparison.
Using middparka's methods, you can transform each image into a sequence of numeric values and then use the Levenshtein algorithm to find the closest match.
I would suggest, like middaparka, that you do not downsample to a 1 pixel only image, because you loose all the spatial information. Downsampling to 16x16 (or 32x32, etc.) would certainly provide better results.
Then it also depends on whether color information is important or not to you. From what I understand you could actually do without it and compute a gray-level image starting from your color image (e.g. luma) and compute the cross-correlation. If, like you said, there is a couple of images that matches exactly (except for color information) this should give you a pretty good reliability.