I suggest leaving the weekends and holidays in your calendar and use the networkdays function to calculate the number of workdays. See this blog post for more information: http://yahqblog.blogspot.nl/2010/09/qlikview-working-day-functions.html
This discussion may be of interest too: http://community.qlik.com/thread/13984
Note, there is no function that returns holidays or can tell you if a date is a holiday. Holidays differ very much per country/region. You'll have to find a list of holidays that apply to your situation somewhere and load those into qlikview.
That's quite an innovative question I'd ever seen on the making of the calendar control. Though I can't offer any good solution, I also feel curious on this topic. Hide weekends in calendar are some features of the control, don't know if these kind of function will contribute goods to this question or not.