I can't say for sure if there is any 'swap' activated at boot time. All I have done for the Linux swap file, is have Gparted create a 256 MB space on the thumb drive.
This sounds confusing...
gparted could be used to create swap
partitions but hardly would get involved to create swap
files.
If you search the web, there is a gazillion of tutorials how to create and manage swap space under Linux
Particular to core is that swap partitions get auto scanned for at boot, while a swap file should be named "tc.swp" in combination with boot code:
swapfile{=hda1} Scan or Specify swapfile
Q: What is a bare minimum amount of 'swap' and what is the syntax to activate it at boot time?
The bare minimum depends entirely on needs created by particular usage, you should rather ask yourself what is the bare minimum of extensions to be loaded onboot.
Should you ever want to hibernate, then there will be a minimum of swap space, but even the size for that is usage dependent.