Although a direct answer to your question is possible, it may be helpful to look at the history of these words.
I was taught that back when male nurses were rarer, 看護婦 was used as a catchall term when the gender of the nurse was unspecified. It sounds old-fashioned or politically incorrect when used this way now, and 看護師 has become much more common.
This is backed up by wikipedia, which states that nurses of both genders were defined (legally) as 看護婦 in 1948, later divided into female 看護婦 and male 看護士 in 1968, before being merged to the general term 看護師 more recently in 2002.
To answer your question, you're correct about the gender implications of 看護婦 and 看護士, and the female variant in particular is still used by some, colloquially. That said, I believe the most common modern term for all nurses is 看護師. The more correct way now if you still need to be gender-specific would be 女性の看護師 and 男性の看護師.
Warning: what follows is pure speculation on my part
As for WWWJDIC's definition of 看護士, I personally have never seen 看護士 refer to a non-male nurse, and would consider this to be incorrect, so I'm not sure why the definition says "may be...". Perhaps this is something to do with the fact that the pronunciation is the same as 看護師, and the change of terminology described above has led to some confusion? I remember even my teacher struggled to explain it at first.