How to sample without replacement from a script that randomly extracts 200characters using shuf?

I have this script that extracts 200 random characters from a set:

#!/usr/bin/bash
n=$(stat -c "%s" newfile.txt)
r=$(shuf -i1-"$((n-200+1))" -n1)
 output.txt

I know shuf is very powerful but I want to include a sampling without replacement. This means that each 200 character extraction has only one chance to be selected when sampling. Output should look like this:

>1     
GAACTCTACCAAAAGGTATGTTGCTTTCACAAAAAGCTGCATTCGATCATGTGTATAATCTAGCAAAACTAGTAGGAGGAGCAAAATACCCCGAAATTGTTGCTGCTCAGGCAATGCACGAATCAAACTACCTAGATCCTAGG
ACTAATAGTGTTTATAATGCCACAAATAGAACTAATGCTTTCGGTCAAACTGGTGAC
>2     
GCCTACCGCATAAAACAGCATCACCGCCACGGCTTCAGGGTATTCTCCAATGGCAAAGGCTCCCATGGTCGCGATGGACATTAAGAGAAATTCAGTAAAGAAATCTCCATTTAGAATACTTTTGAATCCTTCTTTTATCACCG
GAAAACCAACTGGGAGATAGGCCACAATGTACCAACCTACTCGCACCCAATCTGTAA
>3     
GCACGTGTCACCGTCAGCATCGCGGCAGCGGAACGGGTCACCCGGATTGCTGTCGGGACCATCGTTTACGCCGTCATTGTCGTTATCGGGATCGCCCGGATTACAAATGCCGTCGCCATCGACGTCGTTACCGTCGTTCGCGG
CATCGGGGAAGCCGGCACCGGCGGCACAGTCATCGCAACCGTCGCCATCGGCATCGA
>4     
GCGTTCGAAGCAATTGCACGAGACCCAAACAACGAATTGCTGGTTGTTGAACTGGAAAACTCTCTAGTCGGAATGCTTCAAATTACTTATATTCCCTACCTGACACATATTGGCAGTTGGCGTTGTCTTATAGAAGGTGTTCG
AATCCATAGTGACTATCGTGGACGAGGTTTTGGTGAGCAAATGTTCGCACATGCGAT
>5     
GTTTAAGACTAACAGCAATCTGTAAGGACATAGGTGCTGGAGTTGAGGTTAGTCTGGAAGATATGATCTGGGCAGAGAAATTGTCCAAAGCAAACACCGCAGCAAGAGGTATGCTAAACACAGCAAGAAGAATAAGTAATGAT
CCTACTGATTCTTTTCTGAATGAGTTGAATATAGGAGACCCCGACTCAACTCATCAT

The input file is a ~8G file that looks like this:

CCAAGATCGCTGGTTGGCGAATCAATTTCATAAACGCCTACGCTTTCAAGGAACGTGTTAAGAATGTTCT
GGCCGAGTTCCTTATGAGACGTTTCGCGTCCCTTAAATCGAATAACGACACGAACCTTGTCGCCGTCATT
AAGAAAACCCTTTGCCTTCTTGGCCTTAATCTGAATATCACGGGTGTCCGTTACAGGTCGCAACTGGATT
TCCTTGACTTCAGAAACAGACTTACGTGAATTCTTCTTGATTTCTTTCTGACGCTTTTCATTTTCATACT
GGAACTTGCCGTAATCAATGATCTTACAAACAGGAATATCACCCTTATCAGAGATCAATACCAAATCAAG
TTCGGCATCAAAAGCGCGATCAAGTGCGTCTTCAATGTCGAGGACCGTTGTTTCTTCACCGTCAACCAAA
CGAATTGTGGAGGACTTGATGTCGTCTCGGGTACTAATTTTATTCACGTATATGTTACTCCTTATGTTGT

Any help would be appreciated. Thanks in advance.