You might have wrong impressions about the file and how it works.
1. Disassembly
This term doesn't mean dividing a file, it is widely accepted as a term for converting machine code from binary form to text form.
2. Extraction/ripping a file
In the past, finding files of known types within a container file was called `ripping`, and there were several `ripper` tools for that. Today, it's usually just called `extraction` and the one tool which became de facto standard for that is `binwalk`.
3. I tell you what you want, what you really really want
I doubt this firmware contains a stand-alone updater which it extracts and runs when needed. If it does, you can catch that in action - ie. reboot the machine in correct moment. But I'm pretty sure you'll find out there's no such mechanism.
If you want to flash another FW using this utility - then just replace the FW inside the file with yours.
How to find it - use your brain, and compare the FW you have with the content of updater package. If there's a magic value, `binwalk` can be persuaded to search for it.
How to overwrite it - this is usually done with `dd` utility.