Hey Phillip-
This is where logic could never be more vital to use in this situation. There are a few facts that need to be addressed here that I know you are aware of "logically", however your emotional tie to her has you thinking the opposite of what you should be doing with regards to this matter.
For starters, isn't she the one who broke up with you, set you free, or otherwise fractured your heart? Take your time in answering this...I want you to be open and honest. Please tell me that this is correct...LOL! Plus, she told you directly, that she won't let it affect your friendship with her.
If these points are valid then why would it be a crime, sinister or otherwise ruin your chances of getting her back by going out on a first date with a new friend?...and someone you don't even know?...and from a dating site?...which by the way, always winds up being an "interview" date anyway. Really...how much progress is really made from an "online" first date?
I say all that to say this...logically, it doesn't matter about the date at all. It's not like you are looking to "score" with this date...how do I know that? Look where your heart is right now. Do you understand? Emotionally speaking, you are thinking that it will screw things up. Logically speaking, it just makes perfect sense.
Guess what? She sees it as perfect sense too. But here's the catch that you'll get from the hook. Because YOU were logical in this, SHE will get emotional, which creates her attraction for you and this, my friend, WILL draw her to you...BINGO!
It is counter-intuitive...you do the opposite of what you think you should do.
I suggest you create "new" friendships, even if they are "online" and date if you are comfortable with it. It isn't going to hurt and it will boost your self-esteem and confidence in the process as well.
Another point I want to make is that you have history with her and a great friendship/relationship to boot. Do you really think that she wants to be relegated to the same rank as the other "girl" friends you acquire? Not a snowball chance in Arizona! Trust me, she wants to remain a special part in your life.
You're on the right track here, Phillip because you are, instinctively, asking the right questions.
The greatest part of all...these actions are actually a stepping stone to winning her back.