Is there a SnagIt portable app for USB or telephones to make screenshots?
No, there is no portable version of SnagIt. I have checked the official website, but the only download is linked to the version that installs on your computer. This is a shareware product, and portability doesn't make sense, since you will have to register it, and the serial keys don't allow multiple-installation.
Full version: https://www.techsmith.com/download-snagit-win-thankyou.html