Succinct word or phrase to begin quoting approximately what someone said

If you're being informal:

Socrates was like "I'm smart because I know that I don't know much."

Tyler was all "Success breeds a hidden failure."

In at least my idiolect, "was like" as opposed to "said" is precisely to indicate that the source is being paraphrased.

Like — Oxford Dictionaries

adverb 2. (informal) Used to convey a person's reported attitude or feelings in the form of direct speech (whether or not representing an actual quotation)

"so she comes into the room and she's like ‘Where is everybody?’"

To quote approximately is to paraphrase:

a restatement of a text or passage giving the meaning in another form

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In order to use this word, you'd have to restructure your sentences:

To paraphrase Socrates: I'm smart because I know that I don't know much.

To paraphrase Tyler: success breeds a hidden failure.

Instead of going out of your way to make it look like a quote but then disclaim that it's an exact quote, you can indicate that you are paraphrasing what someone else said by avoiding making it look like a quotation in the first place.

For example, if you are talking about something another person said, use the third person to indicate that you are restating what they said, and not directly quoting them. Instead of:

Bob said "I am going to the store."

you can say:

Bob said he was going to the store.

Both convey the same meaning, that Bob intended to go to the store, but the first implies a specific wording was used by Bob, and the second does not.

For your examples, you could write something like:

Socrates said that he was smart because he knew that he didn't know much.

Tyler said that success breeds a hidden failure.

More colloquially, I've heard more or less.

Socrates more or less said I'm smart because I don't know that much.

More or less, Socrates said that I'm smart because I don't know that much.

He said I'm smart because I don't know that much, more or less.

This phrase indicates that you're paraphrasing, or that you're 'reading between the lines', e.g.: