I think you should make like your username and just go into this meeting with an open mind.
I don't think you can plan these things too much. You might meet Cindy and feel no attraction. You might meet her, realise you're interested, but it might not be reciprocated. You might find that you get on as friends. You might not get on at all. You can't control any of these things, or force the situation to develop one way or the other, so just relax.
With regards to being freaked out by seeing them being affectionate (or worrying about her being upset by your interactions), well, that you can do something about. Talk to your partner, gauge her opinion on what she thinks Cindy can handle, and have a good think about what level of interaction you are comfortable with at your end. Make sure you have the ability to either communicate in the moment if you are feeling bad, or have a way to just extract yourself from the situation. I think it's ok to not have a clear idea of what your personal comfort level is when meeting for the first time, but that doesn't mean you just have to keep a stiff upper lip and sit through something that feels uncomfortable either. That will probably do more harm than good in the long run. Make sure you explain that to your partner.
Hope it goes swimmingly!