The coefficient of variation (CV) is just the standard deviation (SD) divided by the mean,. Often, although not necessarily, it is expressed in percent terms. (A referee of a paper of mine commented that a CV of 2 was extraordinarily low. He was presuming that I meant 2%. It really was 200%.)
As you are aware, the mean and SD both adjust for sample size. That is, the totals of 1 2 3 and 1 1 2 2 3 3 are quite different, but dividing the totals by the sample sizes of 3 and 6 is precisely what ensures getting the same mean. A similar but not quite identical argument underlies the calculation of the SD.
Hence the CV carries over an automatic adjustment for sample size.
What remains are general and specific warnings.
Generally, all measures are subject to sampling variation, so keeping an eye on the sample size being used is always prudent.
Specifically, the coefficient of variation is highly labile at the best of times. That follows mostly from its being a ratio and hence especially sensitive to variations in the mean as well as the SD.
In your circumstances it sounds as if you are obliged to use the CV, but several threads here underline its limitations. See for example this thread and others highly voted under the tag.
The bottom line for you is that you have a high risk of making the wrong decision, especially if your sample size is much smaller than that used in the previous study. One way to get a handle on the risk might be to bootstrap the CV calculation for your data.