No, one of those knocking about will not do. Purists may stop reading here
but to make it simple, what you need to do is to make the output from one computer talk to the input of the second computer, and vikki versa.
Maplins sell crossover cables like this one:
CAT 5e Cross-Over Cables : Network Cables : Maplin
and if you want to read a rather more technical explanation you can find a Wiki entry here:
Ethernet crossover cable - Wikipedia, the free encyclopedia
But, yup - I'd use the pen drive solution too in your situation, if you have one.