Mesaana could have channelled a protective layer (like gloves) not to touch directly the OR. It's theorically possible, but she would have been surrounded by sisters looking closely at what she was doing (and ready to shield her if she failed the test).

However I think there's an even simpler way to achieve the same result. Not only Mesaana had to hold the OR, but she had to channel a thread of Spirit into the numerals to activate it (it seems the person to be bound must be the one channelling or at least it's how the AS do it? I'd have to reread the scenes with the OR involved to be sure).

It was thus all too simple to weave inverted Illusion, a very simple and limited Illusion, and appear to channel into the Binder's numerals while in fact Mesaana's thread of Spirit touched not the numerals on the binder but right next to them. So Mesaana could have sworn the Oaths on an inactive Binder...

Luckers's scenario works for me too, though. Another alternative is that Mesaana abandonned her sister alias that day, killed a novice and took her place. We don't know what she plans to do by remaining in the Tower, and perhaps a disguise as a novice or servant would be enough now. Eventually, Egwene and the Hall will have to realise they must test all the novices too. There's like a thousand of them, we know some BA came to the Tower already as DF and it might be the case for several of the current novices too, and Verin's hunt was covering only the 40-ish novices in the Tower before the coup.

Nowadays the novices are taught to link and from circles for defense. Many of them have seen AS weave defensive weaves (in the rebellion) and now many have seen Egwene use the OP as a weapon. They are also not bound by any oath. They can lie, they can kill with the OP if shown how, and the AS don't fear anything from novices. Perhaps there's no or few DF among the 1000 novices, but if there are they might be used as fairly dangerous backstabbers during TG. And Mesaana is an expert at turning young minds to the Shadow. She had managed to put herself in charge of indoctrination into the Shadow in most territories held by the Forsaken in the WOS (not only her own). She might not look like much, but she's a clever and devious woman. She let the other fight over who would run the show in the here and now, meanwhile she was shapping the next generation of Chosen and FoD, educating them according to her worldviews and desires, organizing them as she chose, and making them loyal to the people working in her educational system. Had the Shadow won (and Shai'tan not destroy Creation as Moridin says he plans...), Mesaana would have become a major power to reckon with as the years passed, which Demandred and Semirhage probably factored in when they chose her as their ally.

Personally I'll be very surprised if Mesaana has not indoctrinated at least a few novices during her stay in the Tower (especially since the number of novices in TV increased spectaculalrly - tripled the pre-coup number or so - despite the Tower conflict and despite the fact Elaida made no effort to recruit, the way the rebels did. Was one of Alviarin's "errands" a tour of DF circles to pass the orders to send their girls to TV for testing? Maybe. or maybe Mesaana worked with those she had at hands. If she is Danelle (a young Brown), that gave her a privileged access to novices, especially once most of the Accepted went with the rebels, meaning the younger sisters would have had to take over their classes.

I get the feeling it's not a coincidence Jordan created a special relationship between Egwene and the woman who knows the Tower novices the most on the one hand, and on the second hand created a special relationship between Egwene and those novices too. She was also always very involved with Sheriam and the recruitement efforts. Jordan even put a bunch of her friends among the novices, and created a storyline with Nicola. That amounts to a massive lot of connections between Egwene and the novices - it's like everywhere she turns it comes back to that (even in TGS, where Egwene used them as her "army". That tends to make me very suspicious RJ had something up his sleeve about the novices, which would make sense since he put in the White Tower the Forsaken who specialized in using young people, and made her lose the whole BA right before TG.