No paper trail? I'm pretty certain they already use email and digital documents. Allowing them to hotdesk (as this is essentially what it is) is hardly a way to prevent employees establishing a paper trail.
Indeed, I worked for a financial company that had a 90-day default purge on all e-mails and chat. You could drag some e-mails to a retention folder ( limited in overall size ) but as far as I recall that only protected them for another finite span of time.
Anything that needed a longer persistence had to be typed-up into a document and stored in Sharepoint, which was more manageable in terms of legal discovery than individual e-mails.