well, i know if you disable ARP, then each system on the network needs to have every other system's MAC address and corresponding IP entered into its ARP tables manually. If you are prepared to do this (which, if you have a small network, is quite doable), you can run
arp -s xx:xx:xx:xx:xx:xx 126.96.36.199
where xx:xx:xx:xx:xx:xx is the remote machines MAC and 188.8.131.52 is its IP address. Remember that the system on the other end will need the same kind of config but pointing back to your 10.2.2.1, and if it's ssome sort of embedded device it may not give you access to such a low level kind of interface, in which this won't be possible.
You could also use the "ip" utility to disable ARP on the interface (ifconfig would show NOARP for it), but the same kind of ARP commands would still need to be run.