It's very unlikely, because the ozone mixing ratio (mole fraction) is of order 10**-6 and the attenuation of the cosmic ray flux is dominated by molecular nitrogen and molecular oxygen.

Dear Lanre,

Some scientists claim that cosmic ray can change clouds and weather but the effect seems to be less than 10% of the current global warming

https://iopscience.iop.org/article/10.1088/1748-9326/8/4/045022/pdf

If this true than since temperature affect ozone hole it would be very difficult anyways to relate ozone layer with cosmic ray. However, if solar eruptions are present, solar proton event and energitic particle precipitation(EPP)can occur and reduce ozone in the ozone layer by few %. I have a paper on that matter and I computed that during the EPP event of 2003, 5–6 DU (Dobson Units) was lost due to this phenomenon which represents 1-2% of the ozone layer. So the effect exists but it is small.

https://www.atmos-chem-phys.net/10/1739/2010/

So to asnwer your question is likely to be NO, cosmic ray is NOT a good mean to evaluate the ozone layer.

Hope it helps