desktop + browser app, need dig signing?

I'm building a desktop app that will SellExecute the browser. At a certain
point, the browser loads a remote page, which calls a (locally installed)
ActiveX control, and the control in turn ShellExecutes another program.

If I register the ActiveX (dll) during the installation of the desktop app,
is there any need to sign the control, e.g., to ensure that the control is
allowed to call ShellExecute?  (My tests suggest "no," but I'm not a
security guru.)

TIA