Safe mounting of decorative hook with small holes
A bit wider than 7/64&quot; (0.109375&quot;) is likely suited for a #4 (0.112&quot;) wood (or sheetmetal) screw. #3 (0.99&quot;) will definitely fit.
Or just take the hook to the hardware store with you to be sure of screw size.
Note that most of the force on such a hook will be down, not out - or shear, not tension.