Kurtois wrote:Is this the solution you are advocating versus using Hazel's uninstall (see image): …
That's how I'd do it.
Should I expect to have to reinstate any license information?
Nope. The ~/Library/Application Support/Hazel folder (which contains the license, rules, etc.) will be retained if Hazel's Preference Pane is removed using the method shown in your image.
I recommend keeping a permanent "database" of software licenses and personally use 1Password for that purpose.