Backup! Backup!! Backup!!!
Make 3 backups if all your important data, photos, tax information etc. Before you do anything. Selecting the wrong partition by mistake will delete everything in it.
Answers
Will the aforementioned article work if I want to say format and split
the shared partition into two partitions; one maintaining the original
purpose of shared media and the other becoming encrypted and requiring
a password to mount and access?
Yes. It should work.
Are there any steps I need to skip because those steps would overwrite
any other partitionion
Note, Step 2 Format Disk Partition as LUKS uses the whole disk /dev/sda
. If you do that, you will lose all the the partitions and the data in that disks. That is you will lose the Windows, Ubuntu and the shared partition as well as any system and recovery partitions.
You have to determine which one is is your newly created partition. Say your shared partition is /dev/sda7
. You shrink it and create a new ext4 partition. I will call this new partition /dev/sda11
. Your new partition will be numbered differently. You have to make sure you use the correct partition number. I would use:
sudo cryptsetup luksFormat /dev/sda11
A mistake will overwrite the wrong partition. See above about backing up your data.
If you have a NVME SSD your partitions will have names something like /dev/nvme0n1p11
.
I recommend you just complete steps 1, 2, and 3. Skip the rest. That way the encrypted drive will not be auto mounted. You will be able to mount it when you need with a click of an icon and by entering the passphrase when prompted.
You should see something like this on your desktop:

When you click on it, you will prompted for the passphrase:

Step 6 creates and saves a key file to decrypt the partition. This key file, called the volume-key
in the tutorial will be stored in the /boot/
folder of your Ubuntu system partition. Someone with skills may be able to get the key using a live USB and get into your partition.
And will that in essence prevent a liveboot USB of Ubuntu from
accessing that partition?
Yes. The data in the encrypted partition will be safe.
Hope this helps