Avoiding spicy food while touring South Korea

There is no reason to be worried. I have read the same kind of articles before going to South Korea. Once on the ground, I noticed that you can indeed find spicy dishes, really spicy ones. But you will also naotice that a huge majority of Korean dishes are not spicy. If you don't touch the Kimchi that is served in virtually any restaurtant as a side dish you should be fine.

I spent quite some time in non touristy places and there was never a problem in this reagrd. My experience was that when I tried to order something spicy, the waiters tried very hard to explain me (by any means whatsoever) that a certain dish is spicy and sometimes even to dissuade me to order it.

To sum up, I can totally agree with what your Wikivoyage article also says:

A common perception amongst Koreans is that foreigners simply don't like spicy food, so you might have to spend some time convincing people otherwise if you really want to eat something hot. Also, while Korean food undoubtedly has the neighboring bland-dieted Japanese and northern Chinese breathing fire, if you're accustomed to (say) Thai or Mexican food you may wonder what the fuss is about.

Yes, you can avoid eating spicy foods. There are mainly three types of solutions in avoiding spicy foods in South Korea.

Restaurants

Some of the foods there are not spicy as much. These include Samgyetang, Kalguksu, Seolleongtang, etc... Kimuchi is always served as a side dish along with some more, but you can leave them untouched.

Almost all waiters in local restaurants don't speak even a basic English. In my experiences learning a basic Korean won't get you much rewards since you don't understand their response. For example suppose that you say you don't like spicy food, and a waiter said something like "This is not spicy so do you try?". How can you know what the waiter is talking about? Add to it the fact that Korean language, an isolated group of language families, is notoriously difficult for any speakers around the world.

Fortunately many restaurants in touristy places display photos as well as English descriptions in its menu, so it should be a decent clue for you. I may recommend that you memorize some non-spicy foods in advance, in Korean as well as English.

Cafes

South Korea is full of cafes (including Starbucks). Especially Seoul has arguably more cafes than any cities in the world. Many cafes are open after midnight in hot places such as Hongdae, Gangnam, and Dongdaemun so you can eat even late at night. You can order sandwitches, pancakes, a variety of cakes, waffles, breads, even salads, pastas and lasagnas (but rare) but some of them may be too sweet for everyday meal (actually I do, though).

Convenience Stores

Like China and Japan, South Korea is full of convenience stores. It is clear to see which food is spicy from the packages.

Since you know much about Japan, I will share my tips in regards to the difference between the two.

Unlike Japan, where leaving food may not be appreciated by some people, you should feel free to leave the food in Korea.

Most people in both countries speak little or no English, but while most Japanese people try to understand your English with smirking faces, many Korean may not reply in English and instead speak Korean so fast. Some might even ignore you. This would rarely happen in touristy places like Myeongdong, Dongdaemun, or Garosugil but did so often on me around the Gangnam station and the entire Incheon.

Compared to Japan, especially Tokyo, there are far fewer Western restaurants in Korea; most are local Korean restaurants with some, but not many, Japanese ones. There exist some Chinese, Vietnamese, Thai, and Italian restaurants but you shall search for them in advance as just walking across the street won't get you any of them easily.

The acceptance of a credit card should be 100% with the government regulation, so you can just hand in your card and then don't need to bother to care about the charge.