Using the Visual Studio Coded UI Test Recorder or the CUITe Object Recorder are not required; the Coded UI test can be manually written from scratch.
What is the full error\exception and stack trace?
The syntax, "new CUITe_HtmlEdit(...)", is only used within an object\ui repository class.
Otherwise you will have to use the syntax, "bWin.Get<CUITe_HtmlEdit>(...)", where bWin is your browser window (CUITe_BrowserWindow).
You can also try following the Quick Start guide here:
There are also some examples as CUITe integration tests: Source Code > Sample_CUITeTestProject > HtmlControlTests.cs.