The only reason I'll put rates up is if my costs increase - so if I need to do an outcall on NYE or NYD then I think charging a bit extra for travel would be okay.
I think being self employed, if I don't want to work NYD then I just won't, so charging extra on the basis that I'd have to pay myself double time (which is the usual rationale for charging extra on bank hols) I don't think is going to wash.
I think if I wanted to do that I'd probably put myself as not available on NYD but leave my phone on, and then say "Well, I'm not officially working today, but if you make it worth my while..."