Update SQL Server Management Studio without restart
Reference:


Download SQL Server Management Studio (SSMS)


Minimize Installation Reboots

Take the following actions to reduce the chances of SSMS setup requiring a reboot at the end of installation:


Make sure you are running an up-to-date version of the Visual C++ 2013 Redistributable Package. Version 12.00.40649.5 (or greater) is required. Only the x64 version is needed.
Verify the version of .NET Framework on the computer is 4.6.1 (or
greater).
Close any other instances of Visual Studio that are open on the
computer.
Make sure all the latest OS updates are installed on the computer.
The noted actions are typically required only once. There are few
cases where a reboot is required during additional upgrades to the
same major version of SSMS. For minor upgrades, all the
prerequirements for SSMS are already be installed on the computer.