Well there might be a way as he asked "without adding lansweeper to the login script or deploying it via gpo".
Create a file hostnames.txt with the hostnames one per line, then execute something like:
FOR /F %a in (hostnames.txt) Do lstrigger.exe server %a domain
Just pay attention, if any computer is offline Lansweeper service will report a scan request made even without contacting the client.
Of course you have to subscribe Premium to have that command.