Vegas may actually let you *write* the 7GB file directly onto the stick, but it won't be readable.
Trying to copy it from Windows explorer to the stick will fail.
There are Mac utilities that can mount NTFS for reading.
I don't know what your compressed file size would be in Handbrake, but you will be able to get it below 4GB without much of a quality hit.
(Handbrake has a "Large file size" compatibility checkbox but it won't help your circumstance. You will still need to get it below 4GB to use on FAT32 media.)