Just to mention first that you could bypass cron altogether with this little trick:
Create a scheduled task with the windows scheduler by calling the shell program

C:\\cygwin\\bin\\bash.exe -l -c /cygwin/path/to/shell

otherwise…

• Install cygrunsrv and cron packages from the admin bundle (with 'Install from internet“ option)
• From a Cygwin prompt, to install the cron daemon as a service type:

cygrunsrv --install cron --path /usr/sbin/cron --args -n

• Start the cron daemon from a Windows prompt with:

net start cron

or from a Cygwin prompt with:

cygrunsrv --start cron

Now change the properties on the service to run as a user other than “Local System”

Run this from a Cygwin terminal

cron-config

Show system log of possible problems from the cron daemon (service)

/usr/bin/cronevents

Check installed modules

cygcheck.exe -c

Check current status

cygrunsrv -Q cron

If you get

(CRON) error (can't switch user context)

this means that the cron service is trying to run jobs as the “Local System” account. Right-click on the service and change the user it runs jobs as to be the one you want.