If you sell the computer without a hdd this means that they will also not have a operating system. If this computer is a couple of years old it's not going to be worth much in that condition. Why don't you wipe the drive with an application like DBAN
and reinstall the operating system. When the hdd is wiped it overwrites the entire hdd, for conventional recovery methods this will mean that the information will no longer be recoverable. But... short of physically destroying the hdd there are forensic recovery techniques that still can recover information from the hdd, but this is very expensive! If the only information on the hdd that you are concerned about is your browser history you would be able to rest easy after wiping the hdd.