Is it possible with Nmap (or other tool) to scan a range of private IPs (let's say 10.0.0.0/8) but being outside any private network (using those IPs) ?
Not using a VPN or some other way to be connected as if you were local the answer is no but not because of a limitation in Nmap or any similar tool. The primary reason this won't work is because the IP range you are talking about, 10.0.0.0/8, is considered a private internet address range per RFC1918 which is not supposed to be routed over the public Internet. In almost all cases this means it will likely be Null-Routed by all the Internet Service Providers routing traffic between your location and the potential target IP's and you will get "no route to host" warnings at best.
That said there are many situations where networks are misconfigured and some connectivity leaks out a very short distance. I've seen this on small providers of metropolitan Ethernet networks and also with misconfigured MPLS networks but these were technically local connections to where I was and not something that could have been reached over the global Internet at large.