During testing we have removed the installer entries from the registry on a managed PC.

Therefore, Pulseway is not listed on Add/Remove Programs.

How do we now uninstall Pulseway?

Try using the Pulseway installer MSI file. When you run it, you have the options of repairing or removing Pulseway. If removing outright doesn't work, trying repairing and it might bring the entry back into the Add/Remove Programs window.

I have purposely hidden Pulseway away from that window on our employee computers to avoid any "misclicks" that would uninstall Pulseway and that's the method I've been able to consistently use to uninstall it.

Put back the registry entry or use PowerShell to grab the uninstall string and script the uninstall. 

You can use this Powershell script:

try
{
	$result = Get-WmiObject win32_product -filter "Name LIKE 'Pulseway'" | Select-Object IdentifyingNumber;
	[string]$a = $result.identifyingNumber;
	msiexec.exe /X $a /qn
	Remove-Item -Path "HKLM:\SOFTWARE\MMSOFT Design" -Recurse
	Write-Host "$a Uninstallation completed successfully"
}
catch
{
	Write-Host "Uninstallation failed"
	Break
}