You describe a procedure for selecting a set of features at fixed hyperparameter values. You do not say what you do, if anything, to optimize the hyperparameter values.
As long as you keep an independent test set not used for any sort of optimization, you are going to get an unbiased estimate of the classifier accuracy on that set. There is no overfitting in that sense.
You should keep in mind though that the 10-fold estimate of the model accuracy for the optimal feature subset is going to be biased high because the 10-fold estimate is what is being used to perform feature selection.
Some overfitting is inavoidable since sequential feature selection is greedy by nature. For example, if you start with an empty set and keep adding features as long as accuracy goes up, you are most likely going to end up with more features than necessary. The increase in accuracy may not be significant, but the feature is added to the optimal set anyway.