This woman asking the question has received so many lumdishe hair splitting arm chair psychology pieces of advice, I wouldn’t be surprised if by now the shiva is over.
I suggested common sense. It’s your neighbor, they are sitting shiva , don’t agonize forever over it.
Just go.
As someone who has recently sat Shiva, I think the focus on “common sense” and not to bother “agnonizing over it” is abhorrent. A Shiva visit is not a social call. We don’t go because WE don’t want to do due diligence and “agonize”; it’s not about us. It’s about the mourner.
In certain circles, visits are not made to individuals of the opposite gender. In others, it is appreciated when the visitor (of opposite gender) says the Posuk but does not sit down. In yet others, a regular visit is perfectly fine. What counts is not the prevailing feelings of all and sundry, but those of the mourner. Will THIS mourner be thankful for such a visit? Will THIS mourner be uncomfortable to be visited by an individual of the opposite gender? All it takes is a simple phone call to another family member to find out. No more than three minutes of your time.
The holier-than-thou “just go” is all about the visitor. And of course, MY opinion. The only feeling that counts is that of the mourner.