Male visiting Iran with younger female companion

I am planning for a vacation in Iran. I am a European Union passport holder and would especially like to see the main architectural sites along the Teheran-Kashan-Esfahan-Shiraz corridor. I am cognizant of current travel warnings (avoid gatherings of crowds, be mindful of when not to take pictures, etc.) and some cultural parameters (respect local dress code, etc.) From the reading I have done so far I am comfortable with undertaking the trip in the near future.

Here is a possible complication: I (a male) may have a female travel companion. She is about two decades younger than myself, blond, and quite beautiful. We are not a couple, so there won’t be an issue with public displays of affection, etc. (a no-go among the cultural parameters, in my understanding). She is basically a friend who is also interested in seeing the country as an independent traveler but does not want to go in alone.

Is this a complete no-go and should it trigger serious warnings? Can I assume that we could stay in same hotels (in separate rooms) and travel on same trains or buses (sometimes in different sections perhaps)? Is there a pattern for older-male-traveling-with-younger-female that we could adopt so that it’s clear we are not arriving on an "illegitimate honeymoon" and that will keep us safe in all (most) situations?

Before issuing default warnings please consider that I am an experienced independent traveler and that (again as far as I know) the situation may be very different e.g. for U.S. passport holders.