Yes, you can refreeze thawed fish without cooking it, but only if it was thawed in the refrigerator, according to the U.S. Department of Agriculture’s Food Safety and Inspection Service (FSIS). Expect some loss of quality when you do.
Frozen food stays safe indefinitely, but once it thaws and warms above 40 °F, bacteria that were present before freezing can begin to multiply. A refrigerator keeps thawing fish at a constant 40 °F or below, which is why fridge-thawed seafood can go back into the freezer. FSIS says seafood thawed this way also stays safe and good quality for another day or two before cooking. Fish thawed in cold water is different: it should be cooked before it is refrozen. A one-pound package may thaw in cold water in an hour or less if you change the water every 30 minutes. Never thaw fish on the counter or in hot water, and don’t leave it at room temperature for more than two hours, because the outer layer can sit in the 40 to 140 °F danger zone even while the center is still frozen.
Source: USDA FSIS, The Big Thaw: Safe Defrosting Methods
Image: Frozen cod fillets, Fumikas Sagisavas, CC0, via Wikimedia Commons.