Its hard for me to think of a colorimetric reaction, specific to just alcohols, and to all alcohols at the same rate, regardless of the carbon chain, for you to build a standard and check with a spectrometer. But maybe one of our real organic chemistry experts knows one.
Seems like you could get a result by IR spectroscopy, but I don't know anything about quantitative IR.
If you have enough sample, maybe you could fractionally distill? You would also get a ballpark number to the general composition, if not the absolute composition. I.E. -- small alcohols have lower b.p than longer ones, the very longest ones may char if you don't vacuum distill, but at least you get those three groups as volumes, and maybe a few more in between.