And it hasn't occurred to your to hire a lawyer? Do you know the term "due diligence"? In the present context, due diligence means getting competent legal counsel, not asking the opinion of HN readers.
And if you don't get competent legal advice, because you are blocking both parties, in the long run they will both win, and you will lose.
Okay then, the best advice is to tell these people that you're waiting for legal advice -- don't do anything on your own. In other words, you don't have to decide, and you shouldn't. Any decision you make independently may be contested by one or both parties, against your interest.
Just say you're waiting for competent legal counsel "in the best interest of all involved parties".
Have you been paid?
On a lighter note - you could unlock them both, then see who gets in first and locks the other out, then you'll have a clear winner! ha!
I think there is something to be said about this approach even if it was said in jest. You might also want to change your own terms and conditions before you do this, to allow you to do this.
I doubt very much if the parties care about you at this point, they are mainly focussed on each other, and if you hand over "the keys" in an email to both at the same time, and resign your role as supplier, with the support of your T&Cs your should be OK.