It is possible to run mstest.exe without visual studio.
Download one of the Agents for Visual Studio ISO’s below and install the Test Agent on the server:
Visual Studio 2019
Visual Studio 2017 (127MB disk space, less than that for download)
Visual Studio 2015 and older: visit https://www.visualstudio.com/vs/older-downloads/ and follow the instructions
This installs everything needed for running mstest.exe from the command line and is much lighter weight than visual studio. ~500mb download and around ~300mb to install just the test agent if I remember correctly.