If we really want to ignore the secular world, that includes not giving their holy days any importance either (except where it involves being mentschlich with individuals of other belief systems) so it makes no sense to think that “nittel nacht” has any spiritual significance. Therefore – no tuma or anything else. Life goes on as usual.
Besides, if you consult the history books, Dec. 25th is the wrong date. It was moved to Dec. 25 to coincide with a pagan festival that the Church Fathers wanted to coopt. We don’t know for sure when the “real nittel nacht” was, so we’d have to observe every evening of the year!