You don't want to just use correlation or linear regression, because you could have two samples that are closely correlated but with one systematically larger or smaller than the other.

You might plot the data against a 1:1 line. You also might look at a measure of accuracy, maybe mean absolute error (MAE), or MAPE or RSME.

In your linear regression model, should "a" be set to zero for the consideration of the "true" relationship between COD and TOC?

Although I have no expertise in your field (Wikipedia tells me these are chemical analyses), I do not think the data you provide can answer the question whether you can replace one method with the other. I see the linear relationship between the two. This relationship appears to be strong and I think with this sample size all tests of sigjificance will yield a significant impact of one variable on the other.

However, using a test to determine the statistical significance of your variables' relationship seems to be beside the point: With large enough sample sizes you will always detect significance, but I think you are more interested in the practical consequences of replacing the variable.

The practical importance can only be assessed when you also incorporate data from how your original variable is used to predict/explain a third variable (or whatever you do with that variable, still no idea, not from the field) and you can then proceed to estimate how good the job is done by the replacement.