OK so in fact the Close button is the Finish button on which you changed the message, and in fact the Finish button is the WizardForm.NextButton with a special finish message.
I confirmed this with this small code :
Procedure CurPageChanged(CurPageId: Integer);
begin
if CurPageId = wpFinished then MessageBox('Finish button caption: ' + WizardForm.NextButton.Caption, mbInformation, MB_OK);
end;
So your intention is to send a click message from inside of LaunchUploaderClick to WizardForm.NextButton object... You don't wish to wait the message to be processed before returning from the program, so you must use PostMessage function.
Something like PostMessage(WizardForm.NextButton.handle,...
with the appropriate other parameters to indicate a click...
I leave it up to you to find what they should be (and to report your findings to help other developpers to know about)...