It's possible to build a portable version of nmap that is somewhat limited (no winpcap), but still usable for a quick port scan.
First you'll need to build the portable package: use a windows machine where you have administrative access.
Download the Nmap windows binary file from here.
Install and run it at least one time to make sure all the DLLs were correctly extracted.
Now you'll have to manually put DLL from the MS VC Runtime in the same directory of nmap.
Now copy the whole nmap installation directory on an USB key, and you'll be able to run it from another machine without installing.