Consider someone who was born to a Jewish father and non-Jewish mother who then converted to Judaism with his mother. It seems pashut from the Shulchan Aruch that one who converts is considered a "tinok shnolad" and therefore has no obligation to mourn for their parents. Therefore it seems obvious to me that aninus is definitely not an issue. The question is that if a convert in that situation would wish to mourn could they mourn and to what extent. The Taz seems to indicated that one may willingly mourn for someone as long as they accept the mourning completely and do not transgress any negative commandments in the process. Does anyone have experience with this type of issue?
The mishnah in Sanhedrin (top of 46b) states that even the family of someone killed by Beis Din, for whom shiva is FORBIDDEN, may engage in anninus, since that is entirely internal. Halacha specifically recognizes internal emotion as a separate sphere or mourning and chooses not to regulate it in this case. It would seem that anninus would be entirely appropriate in your case, but you already knew that. :)
I had an unfortunate situation in a slightly different direction. The direction given us was that no minyan could be held, we could not call our open-house a "shiva," and there were no requirements of shiva placed upon the relatives. It was... okay, I guess. The guideline was passive behaviors were permitted, active ones were not.
HOWEVER, we could voluntarily chose to observe customs of shiva without a formal acceptance since that has no real halachic import. In our case, Kaddish could be said (one of the weird technicalities we dealt with).
But as always, CYLOR.