Currently Jenkins crontab does not support a complicate logic such public holidays exclusion. However, there are some options out there you can use to accomplish that:

First

For my project I create my own holiday database, which it is a file containing the days I want to exclude eg.:

# /path/to/holidays
# New Year's Day
01-01-2017
# Christmas
12-25-2017

and I check it using a Jenkins shell script, as it was proposed here.

For example for the above file format:

#!/bin/bash

TODAY="`date +%m-%d-%Y`"
if grep -q $TODAY /path/to/holidays; then
   echo Skipping holiday for $*
   exit 0
fi

$*

Second

A more robust solution but more complicate is to create your own plugin based on the Run Condition Example Plugin in which you exclude the public holidays of your Country such as this plugin.

I don't think we have a way to unset the short flag on help but if you define your own help flag, we'll automatically do the help action for it and you can leave off the short.