I wrote a utility called "Bits" which does exactly what you want. It installs an Explorer right-click menu that when selected analyses the file and tells you if it’s 32 or 64-bit.
It’s around 5K in size, has no dependencies beyond what is already present on the system and is a single file. The only installation required is to register a right-click menu with Explorer. The installer/uninstaller is embedded in the EXE.
Once installed you simply right-click on the file you want to check and choose, “32 or 64-bit?” from the menu.
You can get it or view the source here: