You can try hping3 to ping using something else than ICMP.
Code:
hping3 www.microsoft.com
This might lead to an alert on your firewall administrator console.
man hping3 for details, there is a lot to read
Arping creates its own ARP packet to broadcast a who-has ARP packet on the network and prints the answers. So it works on ARP level, not IP.
For nmap if you don't want to ping before, you should use -P0