tc-install script supports both 32-bit and 64-bit (pure) in net mode. (download from internet)
If you prefer a GUI interface, you could download that. (tc-install-GUI.tcz)
If you're going net mode, it will create a clean USB with no extensions in it.
The script/GUI will ask for a TCE path to a previous installation.
Please leave it blank, so you won't have 32-bit files in your new installation.
If you want to install via ISO mode, grabbing TinyCorePure64 will give you a Xfbdev as a minimum X server instead of Xorg