What you propose requires some heavier changes to the core unless you know the IPs of the computer you want to set up the private network with.

In case you know the IPs all you do is blacklisting all IPs ( enter "*.*.*.*" ) under options->filter->hosts and whitelist only the IPs of the known computers.

In addition you will have to add the line "USE_GWEBCACHE=false" to your limewire.props file.