Cygwin, cron and Kshell -- please help

I'm currently trying to run a ksh script from cron using cygwin.
The script works perfectly from the command line. But when I attempt simple things like "let" or kshell file existence cheking from cron, I receive the following message:

'let: not found'

'[[: not found'


This script is using the '#!/bin/ksh' to pick up the ksh and I've even changed the oracle user's shell to ksh in the password file.
If anybody has ideas, please let me know. The default shell cygwin comes with is bash.

#!/bin/ksh

let a=0

RemoveZipFile()
{
# Remove previous backup up zip file

if [[ -a f:/oracle_export_data/dmadwp/help.*.zip ]];
then
/usr/bin/rm f:/oracle_export_data/dmadwp/help.*.zip
else
mutt -s 'DMADWP Export could not find zip file to remove. Export stopped' URL' < /dev/null
exit 15
fi

}

RemoveZipFile