Apply KNN from small supervised dataset to large unsupervised dataset in Python
In machine learning there are two broad types of learners, namely eager learners (Decision trees, neural nets, svms...) and lazy learners such as KNN. In fact, KNN doesn't do any learning at all. It just stores the "labeled" data you have and then uses it to perform inference such that it computes how similar the new sample (unlabeled) is, to all of the samples in the data that it has stored (labeled data). Then based on majority voting of the K nearest instances (K nearest neighbours hence the name) of the new sample, it will infer it's class/value. 
Now to get to your question, "training" the KNN has nothing to do with the K itself, so when performing inference feel free to use whatever K gives the best result for you.
I have trained and tested a KNN model on a small supervised dataset of about 200 samples in Python. I would like to apply these results to a much larger unsupervised dataset of several thousand samples.
My question is: is there a way to fit the KNN model using the small supervised dataset, and then change the K-value for the large unsupervised dataset? I do not want to overfit the model by using the low K-value from the smaller dataset but am unsure how to fit the model and then change the K-value in Python.
Is this possible using KNN? Is there some other way to apply KNN to a much larger unsupervised dataset?