Nothing, there is nothing that anyone should worry about.  If anything, you might have a day of confusion if the fork went really off the chain, lol.  There is nothing that is going to hurt your wallets, although a trusted online wallet is the easiest place to ride a fork out as that leaves the site to deal with any issues and not you.  But, make sure that you really trust a site, because potential scammers love to use excuses like this is bail with their clients wallets.