I don't believe the microwire that is used for climbing is the same as the mono-filament for the whip. The weapon is a single strand while the rope is many woven together if I remember correctly.
Not really the point of this thread though...
I believe the answer to the original question falls into the declaration of actions step in how the Action Phase is handled. I don't have a book open right now, but I think everyone needs to declare their actions at the same time if they are acting on the same initiative score. Interrupt Actions are just that, you can use them to interrupt, but Free Actions don't have that luxury. I believe if someone wants to use a Free Action to do something on someone else's turn they would have to declare it first. So, you couldn't use the Free Action to ready the mono whip as part of the interrupt to parry. You would have had to already declare that you were taking your Free Action.
That's my interpretation so far. Again, basing that on memory, not specific rules citation.
