Treat them like they already belong.
As for it-might-look-like-a-date ... ask them to tag along for your mid-day coffee run. Don't ask them out for coffee on a Friday evening.
There's a formula for this kind of thing, but polite professionalism is also a communication skill that needs practice. The formula goes like this: 1. State why you're about to ask for whatever it is. 2. Ask for it.
Assuming #1 definitively isn't "to get a date with this person," then it's really quite straightforward to handle the situation. If they imply that they think you're making some advance, you can literally say "No, wait, I think there's some misunderstanding, I'm not doing that, I'm literally just [repeat your reason for talking to her]." And then make some concession to demonstrate the point, such as "If this would make you more comfortable, we can discuss this out in the common area."
If it's a casual conversation without a strong agenda, you can also just say that. "I don't really have an agenda, but I want to get a sense for your communication style so that I know how to work with you."
I think it might be a bit presumptuous to think that a woman who feels she needs to be cautious just needs to have a contentious guy talk to her, as if she and her presumptions are a puzzle, and being contentious is all that's needed to solve that "puzzle"
As to the question of, "Well, if she's going to be guarded about everything, what do you say?" -- in the context of the current thread, my opinion is that it is nothing about what you say, but the context and setting. Don't ask her what it's like to be in a boy's club or similar small talk while she's working at her desk. Go out for coffee, and bring along another co-worker or 2, if the intention is to make a new worker become acclimated with the rest of the company.