If I were the man it sounds like It’s a bit risky to me. I’ve been a male boss and co worker around all women and it just wasn’t my thing. I had some worldly morals guiding me but I think I floated dangerously close to a mistake one time prior to being Born again. but this Depends on the man and his walk with God. Can he resist the temptations these interactions may bring fourth? Is he a mature Christian who operates in the spirit or is he carnal or worldly in his faith? Satan loves to jump on this stuff because he is a great tempter and accuser and if a man doesn’t see the attack coming he can get taken out easily by it. I think it’s something you won’t find direct scripture for an answer . Something to ask God for wisdom and discernment and walk in step with the spirit. Closest thing I can think of is the OT story of David and Bathsheba. David was anointed by God but it was OT times prior to the work of Christ . Bible is always the bedrock of the faith but we have to begin to trust God within us Holy Spirit on the more complicated things without clear answer. Perhaps someone more experienced than myself will chime in but for now thinking you might read the story of David and Bathsheba
I have been rereading some of the longer replies to be sure I didn't miss anything, and I just want to thank you for your input. A mature and pretty solid believer I know had a situation at work that ended up with him compromising with a women there, much to his surprise and those of us who new him too. He did repent but it got him into a lot of trouble. It was a hard lesson for him to discover he wasn't quite as above the temptation as he had thought he was.
I have been a party to getting to close to the wrong people in the past. And I see lots of people getting into precarious situations with members of the opposite sex because they spend regular time together at work and so on, and end up forming an attachment that isn't healthy.
I was thinking of the extreme end of this, like the basic physical lust issue that has brought men and women in every generation in history, people of sincere faith and held in high esteem within the church, and who hold to a pattern of good morals, way down low.
As in the example you gave, David just saw Bathsheba bathing... I am very certain he had seen MANY naked, beautiful women given his position, the concubines and the wives etc... and yet, that was all it took. To see more of a woman's flesh than he should have seen.
Maybe I am just too old fashioned though, and maybe as some say, it is a matter of personal judgement that the bible says nothing about. I had hoped to see things from different Christian's experiences, and I appreciated the David reference, so this has been very helpful thank you.