Are cooked frozen shrimp safe?
The frozen pre-cooked shrimp are of course safe to eat if they come from a reputable source.

You may wish to cook them a little bit to heat them up to service temperature, and integrate them with a sauce or spices or so on, but you could just peel and eat them if you wanted to.

The shrimping industry may have some variation in how it processes shrimp after they are caught.  There are certainly some vessels that are capable of cooking their fresh caught catch on board; there are also some shrimpers, especially in waters near the US, which can freeze the shrimp on board.  Hopefully someone more directly familiar with the shrimping industry can give you a better answer on this part of your question.

Even if the shrimp were caught, frozen on board, then cooked at a processing plant and refrozen, assuming that the various parties took good and reasonable care, they could still be of high quality and of course safe.

All of the above assumes you are buying shrimp from repuatable and licensed sources in your own jurisdiction.