After installing the Splashtop client apps on your PC, you could copy the installation folder to your flash drive. Then you could run the Splashtop client apps on other computers without installing them again.
Here are the corresponding file paths you should copy:
For Splashtop Personal, C:\Program Files (x86)\Splashtop\Splashtop Remote\Client for STP
For Splashtop Business, C:\Program Files (x86)\Splashtop\Splashtop Remote\Client for STB
When you run the client app off USB, be sure to *not* save password at the login screen. Or be sure to log out of the client app after you're done. This is so your password is not left on the local computer.