The correct answer is none of the above.
The word “walk” is a common noun, which means it does not refer to a specific walk. Therefore, we do not need to use an article (a, an, or the) before it.
We can use the article “a” before a common noun when we are referring to a specific instance of that noun. For example, we might say “I went for a walk in the park.” In this case, we are referring to a specific walk that happened in a specific park.
We can use the article “an” before a common noun that begins with a vowel sound. For example, we might say “I saw an elephant.” In this case, the word “elephant” begins with a vowel sound, so we use the article “an.”
We use the article “the” before a common noun when we are referring to a specific instance of that noun that has already been mentioned or is known to the listener. For example, we might say “I saw the elephant that escaped from the zoo.” In this case, we are referring to a specific elephant that has already been mentioned.
In the sentence “Shall we go for a walk?”, we are not referring to a specific walk, so we do not need to use an article.