This really isn't a fight if The Force can't come into play. A Jedi's strength comes from The Force. And, while his skill at swordplay is superior to the average untrained person, it's crippled without The Force to guide it.
The only hope Obi Wan would have is for his light sabre to destroy her katana, but even that would only delay the inevitable.
Wait, is no force powers only the push and choke and stuff? If so, Obi Wan. All he has to do is see and block one shot, or possibly hack away, as she can't block him. If he still gets force enhanced agility, strength, etc. then he wins. If it was pure swordfight, she pokes him five times in the chest then takes six steps back.
Jedi don't need the force to in saber fight. They get their sword skills by training. The force assits Jedi in preforming powers or feats. But sword skills have nothing to do with the force. They do train. Jedi's do have the force but its not necessary in a sword fight if and when the match is evened up in a sword to sword battle.
Both are good swords-persons with almost flawless techniques. I couldn't call this one. They're both fast, agile, have high endurance and are very skilled with the blade.
So this one beats me truthfully,..thats the only way i can cut it. (no pun intended)
To be fair, Black Mamba has "powers" as well. Pai-Mei's training clearly allows her to perform superhuman feats, ven aside from the Death Touch and low-level Anime Leaps. After being shot with a rock-salt load at point blank range, drugged, buried alive, and crossing miles of deasert on foot with little or no food/water/rest; she was still able to defeat a well-rested and un-injured California Mountain Snake.
She's not in the same league as a Jedi, but she could give one a hard time like Jango Fett did to Obi-Wan. Abandoned by the Force, the Jedi would only stand a chance if she got cocky or failed to grasp what a light-saber was.