The important observation here is that, given that you want to tune a cut off parameter to produce a specific misclassification rate, that parameter is part of your model. Said a slightly different way, choosing the cut off parameter is part of fitting your model. Cross validation should be aware of the entirety of your model fitting procedure.
In practice, you need to formalize a procedure for tuning this cutoff parameter. If you want to tune your cutoff parameter to produce a certain misclassification rate on your training data, then do so for every fold of your cross validation and evaluate the results on the out of sample fold. As you observe, you will get different cut off parameters for each fold, but this is no issue. You are evaluating a procedure at this point, not a final model. You can then make model selection type decisions confident that you are taking into account the full scope of your model fitting procedure.
When you have finished model selection decisions, you may follow the specified procedure on your entire training set, and then evaluate the final model's out of sample performance on a final hold out.