I may be wrong, but I don't think it's wise to have duplicate contracts. The duplicates are not "copies", they are actual contracts. Even writing "copy" on the second contract wouldn't reassure me. You've got ink on both contracts.
I make sure that as soon as I'm back at the office or back to our home office, I either scan and email, or fax a copy to the clients, or make a copy and put it in the mail.
So what do you do? Tell the client No, you can not have a copy of what you just signed, wait till I send it to you? I've only had a couple of people that wanted copies at signing, and did not have access to email (they were blind buyers, literally). The fastest way was to rewrite the contract so they could show it to a sighted relative. Everything I do is scanned, and archived anyways and always available for reproductions. Its an offer on a property, not the deal set in stone.