Don't know if you're still interested, but there's a little known Microsoft tool, hidden in the Server 2003 OEM Preinstallation Kit CD, that does what you want.
It's a modified version of SYS.EXE, and can be run under modern Windows operating systems (even 64 bit ones). It works only for FAT32 drives, though. Does not work with FAT16.
I use it to create MS-DOS 7.1 bootable USB drives easily. It works really well. (you don't need Rufus, nor the famous HP USB tool)
I'm not sure about the license. I guess it's illegal to post it here, but I can tell you where I found it in a private message if you want.
EDIT: I'll post here the SHA1 hashes, to verify the files if you search for them in google (I think they are old enough to be considered abandonware, though)
d6d930090658820333772a3a5a76af949d95f3dc ?SHA1*2003opksp1.iso (size 387819520 bytes)
0e63d1b5710131d1e3e715871ea86097bb3ff68f ?SHA1*2003opk.iso (size 395771904 bytes)
The first one is for Server 2003 SP1 OPK, the second one is the regular Server 2003 OPK without service pack. But the contents of both ISOs are almost identical.
The SYS.EXE file is located in the "TOOLS\X86" subfolder.