If you place your photo to be copied manually, rather than through a manual feed, you needn't be concerned.
Bright light causes chemical reactions any time the photons interact with a surface, but the brief flash of a copier, one single time is unlikely to be of any consequence.
My wife has been a photographer for over twenty-five years and has used the very similar process of scanning to convert her older photos to digital versions many times without damage to the original. In fact, scanning them or having them scanned to a digital format (jpg, etc. ) may be an even better idea in terms of preserving them.
Unless you have something extraordinarily frail, you should have not problem. If your original is extremely delicate, it should be handled by an expert in such reproductions. But that did not sound like the sort of copies you were talking about.
Like David writes so well the scan from a colour copier will not be that bad. As someone who works in the photocopier industry I know of many libraries, archive and document centres who don't seem to have any problems over a period of time with damage to very precious photo's.
As David says scanning them in detail so a replica can be used so the originals can be preserved maybe of more benefit to the photos in the long run.
In our experience, photographs do not get damaged if exposed to scanning light.
Light used for scanning in the scanner is day light, but very soft.
There is no need to high power illumination since the scanning system is extremely close to the scanned piece.
My recommendation is that you go ahead, scan the images and then use the professional services of a graphic artist to restore the image to original conditions.
Color casts can be neutralized, some hidden areas can be given more light and more detail.
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