Linear Discriminant Analysis (LDA) , Removing colinear features in cross validation set up is correct or not?

My data is a matrix with 725 features and 667 observations which have binary data(either 0 or 1). my target variable is a univariate which has two classes (either 0 or 1). I removed the features which had zero as column sums, so features reduced to 652. since I have a binary data I did not do the preprocessing (Mean = 0 and s.d=1). But, My data is highly sparse; there is 99% sparsity. If I want to use LDA model in a 10 c.v setup. Then I am required to remove the colinear features (this means that all the features in a training set whose column sum is zero should be removed) to predict small set of test data in every fold. If this is the case then in every fold I will have to remove a different set of features which are zero in that training set for the test set. Is it an acceptable practice to complete my y.predict after 10 c.v (each fold used different features to predict the y) and do a rowmean for all the folds in the end and then show the accuracy of a classifier? I cant have the correct feature selection from this strategy but I can get a classifier prediction performance.