|First of all Windows XP has a builtin powerful emulator (NTVDM) to run legacy DOS programs from command prompt or a shortcut. So it is not true Win XP can't absolutely run DOS applications directly.|
If however that fails, you can download for free Microsoft Virtual PC or the open source VirtualBox and install Windows ME inside a virtual disk.
In that way you can run concurrently two operating systems avoiding the harmfull dual boot process.
It is worth to try as it is easier to do than to explain.