If you are only concerned with securing the program's files, then you could use TrueCrypt to create a container, mount it as a new drive letter and the install your clipboard manager there. This way, if someone steals your computer, he would not have access to these files.
Full disk encryption is of course a much better option, because it would protect all the files on your hard disk, in case of hardware theft.
On the other side, securing a program you know nothing about is quite complicated. It is not enough to block the program from using the network. Any other program running on your system may access the clipboard manager's files and send them over the network. So be carefull when installing software from unkown sources.
Besides the general recommendations of keeping your system and your antivirus/antispyware/firewall programas updated I would advise using a simple Clipboard Manager, which offers only the functionality you need. If it is simple it means that less things could go wrong.
Moreover, popular opensource clipboard managers are less likely to contain malicious code, as everyone could detect it by analyzing the sources.