I created a VSTO Outlook Addin that uses a library Html2Xhtml.dll (.NET) which calls another Html2xhtml.exe by executing System.Diagnostic.Process.Start().
However,
Had the same issue for ClickOnce applications. Here is what you need to do to get the deployment path of the addin:
Add System.Deployment.Application reference in your application
next is to use this property to retrieve the deployment path:
ApplicationDeployment.CurrentDeployment.UpdateLocation.ToString()
and there you go!