As COLGeek points out, 64-bit CPUs can run 32-bit OSes - this was common near the tail end of the XP era, and even into the Vista era, because of the extra overhead of 64-bit Windows (it needed more RAM to run the same apps) and the abysmal driver situation for x64.
Also, while you will need to boot from a 64-bit media and install it from there (as the installer on 64-bit Windows DVDs is a 64-bit program itself and will generate an error if run on 32-bit Windows), you do not need to format your drive, the installer will normally dump most of the contents of your boot drive in "C:\Windows.old" and you can restore it from there.
There are still legit reasons to run 32-bit Windows, which is why Windows 10 still exists in a 32-bit version for example. One of them is on low-end hardware, such as tablets, many of which still come with 2 GB of RAM and a 32-bit CPU; the other is for legacy 16-bit apps, as the 64-bit versions of Windows removed that layer of compatibility. Most people who seriously need this should be running it in a Virtual Machine though.
Also, final thing about getting your hands on bootable media for Windows. If you own a legit Windows Vista license, it is legal to download a 64-bit Windows Vista ISO and make a bootable USB stick from it - Microsoft even provided its own tool for the purpose. Have a look here:
https://www.microsoft.com/en-us/download/windows-usb-dvd-download-tool
I don't know if they still supply the ISO files through some FTP service as they used to, though.