What you're asking about is really the guerre de course, commerce raiding. In WWII we saw it employed most prominently in two theaters: in the ETO, by the Kriegsmarine versus the UK, and in the PTO, by the US Navy versus the Japanese. It isn't a coincidence that the primary targets were island nations, but I'll get to that in a second.

The objective of commerce raiding during WWII really wasn't to "disrupt trade" so much as it was to deprive your opponent of the ability to ship critical goods like food, ammunition, fuel, or to move troops and equipment from place to place. There really wasn't a whole hell of a lot of international trade going on during WWII, at least in the traditional sense, but there was a LOT of wartime goods and food getting shipped all over the place. As it happens, two of the major combatants were island nations (Japan and the UK); both were heavily reliant on imports for their war efforts, to maintain their domestic economies, and to feed their population. As such their shipping lanes were extremely juicy targets.

We're probably all most familiar with the Battle of the Atlantic. In short, this was the German guerre de course versus Allied shipping across Atlantic shipping lanes. U-boats were the primary weapon, but surface raiders saw limited action as well. There's a lot of debate, still, on just how effective it was. Of course, Churchill said the U-boats were the "only thing he ever feared" (or something like that), but the numbers really weren't in Germany's favor. Even in their best months they were never anywhere near functionally closing down shipping lanes, so it was essentially a battle of attrition: the Kriegsmarine had to sink more merchant ships than the British could build. Once the British were out of ships, they'd starve, their economy would collapse, and they'd have no more beans or gas or bullets, and that'd be that. Early on (summer of 1940 to the winter of 1941, then again later, when the US entered the war) the U-boats were doing well enough to accomplish exactly this. Then...American industrial might, coupled with a whole lot of tactical and engineering ingenuity, swung the balance back in the Allies' favor, and quickly. New tactics (convoys, and convoy routes), tech (hedgehogs and sonar and so on), equipment (escort carriers and long range maritime patrol aircraft), and tactics made being a U-boat crewman very, very dangerous. The threat was basically ended by 1943, and U-boats were basically mauled until the end of the war.

The Pacific followed a somewhat opposite trajectory. The British had learned how devastating subsurface commerce raiders could be during WWI, and so made sea lane defense a major priority. The Japanese wanted only a DECISIVE BATTLE, and so really didn't pay much attention to protecting their merchant fleet. This was a bad idea, because they needed practically everything needed to live, and to fight a war, imported to the home islands. They went on building their mighty fleet with which to eradicate the US Navy, and just sort of ignored things like escorts, convoys, destroyers, and so on.

Fortunately for them, for the first part of the war in the Pacific, they were saved by the criminal incompetence of the BuOrd and the Mk14 torpedo. TLDR: it didn't work. And it crippled the Silent Service. The reasons for this are all kinds of wrapped up in shady military bureaucracy, but the bottom line was, the US submarine fleet was next to useless for over a year because of their poor torpedoes.

After a while they got things worked out though, and then it was on in a big way. By 1944 they were sinking twice as many tons of merchant ships as the Japanese were building, and the results were conclusive: everything you read about the IJN and IJA during 1944 and 45 is prefaced by "materiel shortages". It ended up being sort of irrelevant due to the atomic attacks, but the sub campaign versus the Japanese was, in my opinion at least, the second best return-on-investment campaign fought by any side during the WWII era.

The best ROI? A related action, called "Operation Starvation". The name was literal. It was a massive naval mining campaign of Japanese ports in the spring of 1945 that essentially brought their merchant shipping to a screeching halt. It doesn't get a lot of attention nowadays because it is something of a footnote between Iwo Jima and Hiroshima, but in terms of effect versus cost, it is one of the best military operations in history.

So, to answer your other question, "did the average vessel actually had much to worry about"...the answer was....yeah. Believe it or not, the US merchant marine suffered the highest casualty rate of any American service during the war. I've not ever seen Japanese merchant marine casualties, but they must be even worse. Strategic effects however, were more mixed.