storing SNPs in the genotype file for each chromosome in a separate file
I believe a pandas approach would be fast enough (probably faster than any other Python approach without pandas).

After converting your table to a pandas data frame, you can do something like df.filter(regex=(".*Chr01")) for the first chromosome then write the resulting data to file with the to_csv() method.

import pandas as pd

data = pd.read_csv('input.txt', delimiter = "\t", index_col = False)

for i in ["Chr01", "Chr02", "Chr03"]:
    regex_pattern = ".*" + i
    print(data.filter(regex=regex_pattern))