Do carrier-less militaries retain the equipment for carrier operations?
Taking the RAAF F/A-18's for example:


  The Australian Hornets were very similar to the standard US Navy variants, but incorporated a number of minor modifications [including] the deletion of all equipment used to launch the aircraft using catapults.


Even though they retain the tailhook, if they landed on a carrier, they won't be able to takeoff.

The tailhook serves the same function as on the land-based F-15 and F-16, provide arrested landing capability for emergency situations.

(Source) F-16 arrested landing.

As for the Harrier, all the foreign operators were navies. So, export Harriers were used on carriers. (Rhyming unintentional.)

The carrier-borne Rafale fighter jet will retain its carrier capability when sold to the Indian Navy.