D6 didn't have a special event in TRadioGroup neither. The OnClick event is is what you need.
D6 help for Onclick:
Usually OnClick occurs when the user presses and releases the left mouse button with the mouse pointer over the control. This event can also occur when
-The user selects an item in a grid, outline, list, or combo box by pressing an arrow key.
-The user presses Spacebar while a button or check box has focus.
-The user presses Enter when the active form has a default button (specified by the Default property).
-The user presses Esc when the active form has a cancel button (specified by the Cancel property).
-The user presses the accelerator key for a button or check box. For example, if the value of the Caption property of a check box is '&Bold', the B is underlined at runtime and the OnClick event of the check box is triggered when the user presses Alt+B.
-The Checked property of a radio button is set to True
-The value of the Checked property of a check box is changed.
-The Click method of a menu item is called.