The Columbia phonograph you described was probably made during the teens to the mid-1920s.
Is it similar in style to this one? >>>

I take it, the sound box or reproducer is fitted with a mica diaphragm? After 1925, Columbia produced the Viva-Tonal series, both in the US and the UK, to compete with the Orthophonic Victrola and HMV "Improved Gramophones" designed to play the newly introduced electrical recordings, which hit the market in mid-to-late 1925. The early UK produced Viva-Tonal models use cabinets similar to the older ones, but the sound boxes are equipped with aluminum diaphragms, and the tone arms are not the straight, bayonet type as in the photo above.
Most collectors I know would discourage playing later 78s, especially those made after about 1940, on a gramophone of this type. (Many, in fact, cite a cut off date of about 1932-1933.) There are a number of reasons for this. In some cases, records produced by certain manufacturers--especially after about 1940--did not have playing surfaces sufficiently hard to withstand the heavy, older acoustic sound boxes and tonearms. Also, the reproducer, itself, is often not compliant enough to track the record groove efficiently.
That said, I've played some later 78s--those made up to about 1945--on both my Victor V, which has an Exhibition sound box, as well as my VV-4-40 (Orthophonic Victrola). But in both cases, the reproducer has been
rebuilt and tuned to ensure maximum performance and efficiency. Also, when playing later records, because of the amplitude of the cut, I always use soft tone needles, which minimize distortion.
As a bottom line, I'd say if these records are not considered rare or valuable, and could easily be replaced if worn or broken, then go for it, as long as the reproducer has been rebuilt with fresh, soft gaskets and properly tuned. This takes for granted that the records you want to play are shellac based and NOT vinyl, which started to take over from shellac in the late 1940s.
HTH,
Joe_DS