Welcome to SolidWorks forums Tofo.
Yes you can do that i.e. have one machine with Internet and use other to give the test. The only thing you would need is some kind of medium (for e.g. pen drive) to transfer data between the two machine.
Apart from this I'm not sure if new test would require to download files or not (if not then you're all good with using two machines). The other thing would be to check if you need latest version or can use SW2010 itself (can not comment on this)
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