I don't know what you mean by "default shell handler". I use XYplorer with it set as the default Drive/Directory handler (where "Drive" and "Directory" are actual names referenced under HKCR in the registry), as detailed
here. TU still opens Explorer.exe on my system.
Edit: Starting in XYplorer 8.90, it's possible to set XYplorer as the default file manager using the GUI. However this doesn't change what happens in the registry, and it still doesn't work with TU.
TU 5.5.1 on WinXP