I can tell you from personal experience this is a bad idea. Native Windows programs cannot accept Cygwin paths. For example with Cygwin you might run a command
grep -r --color foo /opt
with no issue. With Cygwin /
represents the root directory. Native Windows programs have no concept of this, and will likely fail if invoked this way. You should not mix Cygwin and Native Windows programs unless you have no other choice.
Uninstall what Git you have and install the Cygwin git package, save yourself the headache.