Run an exe file that exists on a different server from a SQL Server Job
You could still use xp_cmdshell; however, you'll need to make sure that your SQL Server Service account (the AD account used to run SQL Server) has access to the directory containing the exe file and any other directories that that program may require.

xp_cmdshell runs on your SQL Server itself; you can use it just like any other command window.

If, on the other hand, you need the exe to run on the machine that hosts it, then you'll need to look at other options.