Yes and no: yes you can do this, but no it might not work as you expected. Not all Forkcoins have replay protection, which means they can move on multiple chains when you send one of them. Getting some Forkcoin dust and including it in your transaction prevents that.
Be sure to work your way down in value: sweep your Bitcoin to a new address first, then the most valuable Forkcoin and continue down from there. Also be careful in installing Fork wallets, people have lost their funds by using compromised wallets.