Key Signing Party is not just about random character generation and computers. It's about the chain of trust you create/strengthen by showing your key with a document of yours(and that is valid inside your country, of course).
The question here is: The person KNOWS that will have a key signing party and it does not bring a key or forget to generate one? That is something to worry about, cause there is a level of stupidity that is very high on this person, or he is not aware(even doesn't care) about the event.
Second. The "no computer" rule is another item inside the chain of trust that this kind of event creates: Key signing parties themselves generally do not involve computers, since that would give adversaries increased opportunities for subterfuge. And usb sticks can be easily replaced by attackers the same way a notebook could be turned on with the "hey bro, lemme generate another key cause i forgot mine" breaking the trust.
So, your company is already playing wrong by using massive external storage to exchange keys on a workstation. Unless everyone is looking at the monitor while the fingerprints are transcript to a text file/word document/whatever one by one, i would not TRUST on the members of this party.
tl,dr: If this party will be done with USB sticks, it's better that everyone give the keys fingerprint to your HR(or other management staff trusted by your company board members), and then, they distribute those fingerprints to your team. There are no disvantages on key signing parties, unless there is a computer involved(or document forgery, but that is a matter for parties where nobody knows each other, what is pretty difficult).