Dropping "when" in an adverbial clause renders this sentence ungrammatical?

When has two meanings:

1 I visited him when (specific) I was in Manchester = at the time that; on the occasion that

2 I visit him when (general) I am in Manchester = whenever, at any time that; on any occasion that

(Meaning 2 also tends towards “if”: I sometimes travel to the North. When I am near Manchester I might visit him. ≈ if)

Your examples are all inverted. They are fronted by a type of adverbial – they are all capable of being re-adjusted, which is the test to see if they work.

1. You should be cautious when walking in a dark alley,.
2. Be cautious when walking in a dark alley.
3. Be cautious walking in a dark alley.
4. You should be cautious walking in a dark alley.

For the purpose of your examples, there is no significant difference between “should be cautious” and “be cautious”

Thus the only examples we need are

1. When walking in a dark alley, be cautious.
2. Walking in a dark alley, be cautious.

And both are acceptable although the context will play a part in deciding which is most appropriate.