The only thing I can think of is “dot sourcing” your profile at the powershell invocation.
For example:
powershell -noprofile -noexit -command "invoke-expression '. ''C:\My profile location\profile.ps1''' "
By changing the script that invoke-expression command points to you can place your “profile” anywhere you’d like. Then, create shortcut that launches PowerShell and set the target to the above command.