PsExec does allow for calling the command as a specific user, you just need to pass the -u and -p arguments when call it.
For my use case, I am using the following command to call the CLI command remotely.
C:\Progra~1\PSTools\PsExec.exe \\worker1 C:\\ptc\\IntegrityClient10\bin\im.exe createissue --type="Product Requirement" --port=7001 --hostname=integrityServer --password=password --user=SolutionArchitect --richContentField="Engineering Response=For performance testing. Do not use." --richContentField="Product Requirement Statement=Created for Performance Testing - DO NOT USE"