How to install psql without Postgres?

Oh, yes:

$ sudo apt-get install -y postgresql-client
$ psql --version  
psql (PostgreSQL) 9.5.12

If you don't want to install anything, just download the package https://www.enterprisedb.com/download-postgresql-binaries

Then run unpack and run ./bin/psql No installation.

The package also contains postgres server which you can run at local without installation also. For more, ref https://www.golery.com/pencil/vU