Frederik IX seems to have been a decent man, so could have been a good match for one of the younger daughters. However, marriageable age for men was higher than for women - typically 25-30 - so such a marriage would not be a serious proposition until well into the 1920s.
In any event, Nicholas does not seem to have visited his Danish cousins much after his marriage, so did the girls actually know Frederik? I'm happy to be corrected on this one, but Nicholas's visits to Denmark seem to have come to an end with his marriage.
Ann