In the process of implementing a secure site I ran into this problem.
I found a discussion on the web which mentions some possibilities, though I can't test them right now.
An option in IE will disable the nag. Not the best solution, but better than replacing all DatePickers before deadline!
"There is a browser setting in IE6 to turn this off (not sure of earlier browsers). Check out Tools > Internet Options > Security > Custom Level > Miscellaneous > Display mixed content. By default its set to prompt, reset it to Enable."