cygstart is good, but not really intended for what is being given. You can think of cygstart <filename> as what happens if you double-click something in Windows Explorer, which means that it can open files in the program by default, as well as run executable files. However, both cygstart ... and cmd /c start ... will lose a nice terminal environment, so I recommend using something that launches a new terminal window, like run mintty .
For instance:
man () { run mintty --title="man $*" bash --norc -c "command man $@ " }
will open man pages in new windows so you can view them while still working in the current window.
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