Sequential feature selection is expected to take a long time, especially when dealing with such a large number of features. If your hardware provides multiple cores, you could speed up computation by fanning out to multiple cores (but that would require the Parallel Computing Toolbox).
The right choice of feature selection depends on the classification or regression technique you apply. In this case, you applied nearest neighbors, but with the default distance metric which is Euclidean. If the user has 77 observations and 7000+ features, Euclidean distance is not a good choice. The cosine distance could perform well in this setting.
Or do you really have just 77 observations and 7000+ features? Don't expect a solid model from such a small and feature-heavy dataset!
For your dataset is indeed that "wide", linear techniques are best. Regularized linear discriminant could work well, and we have a doc example showing how to use it for feature selection (see LDA-with-variable-selection for more information) . Another good option would be a linear model with lasso penalty fit by fitclinear using the SpaRSA solver. However, that's not a linear techniques. Did you make a deliberate choice in avoiding linear techniques?
Finally, there is no need to copy the class label variable into the last column in the predictor matrix before running sequentialfs.
