Coordinating conjunction immediately followed by parenthetical — Is a comma needed or not?
Ordinarily parenthesis should be marked with commas on both sides. But Fowler recommends that the first comma should be left out after a coordinating conjunction if what follows is a simple adverbial phrase—if I interpret him correctly. (Coordinating conjunctions are and, or, but, and possibly some semi-conjunctive adverbs like so, therefore, however, etc.) The comma should be retained before a subordinate clause or when its omission would cause ambiguity. This probably includes conjunctions that are not at the beginning of a sentence. Fowler's advice seems balanced and practical.
Cleopatra appeared poised and composed. But on the inside, she was seething with rage. — Simple adverbial phrase at the beginning of a sentence.
Her only option was to support Mark Anthony once again. But, if he should perish, it would be the end of her. — Not a simple adverbial phrase but a clause.
She knew her cause was lost and, in a fit of final despair, had a serpent brought in to extinguish her life with its venom. — Not at the beginning of a sentence.
The relevant text from Fowler's The King's English follows. He is arguing for general laxity with adverbial phrases, and would generally allow both commas and no commas around them. He goes on to say that, if commas are used, one must never omit one but write the other; however, he gives the above rule as an exception, in order to avoid an abundance of commas, logical though they might be.
Laxity once introduced, however, has to be carefully kept within bounds. It may be first laid down absolutely that when an adverbial clause is to be stopped, but incompletely stopped, the omitted stop must always be the one at the beginning, and never the one at the end. Transgression of this is quite intolerable; we shall give several instances at the end of the section to impress the fact. But it is also true that even the omission of the beginning comma looks more and more slovenly the further we get from the type of our above cited sentence. The quotations immediately following are arranged from the less to the more slovenly.
His health gave way, and at the age of fifty-six, he died prematurely in harness at Quetta.—Times.
If mankind was in the condition of believing nothing, and without a bias in any particular direction, was merely on the look-out for some legitimate creed, it would not, I conceive, be possible...—Balfour.
The party then, consisted of a man and his wife, of his mother-in-law and his sister.—F. M. Crawford.
These men in their honorary capacity, already have sufficient work to perform.—Guernsey Evening Press.
It will be observed that in the sentence from Mr. Balfour the chief objection to omitting the comma between and and without is that we are taken off on a false scent, it being natural at first to suppose that we are to supply was again; this can only happen when we are in the middle of a sentence, and not at the beginning as in the pattern Cranmer sentence.
"Well, Stunk's Rules of Usage says that you're wrong. No comma."
"no comma is needed" does not mean "it is wrong to use a comma."
I don't have a membership to the CMS, so I can't speak to their take on it. But I would say that the meaning, or at least the tone that you're trying to communicate it subtly different between the two phrases. In your punctuation, the speaker is expressing doubt that "we are prepared to act promptly", and perhaps expressing the subjunctive as a bit of an aside.
And if the actual meaning is different, then rules of usage be damned. I personally would punctuate it thusly:
The situation is perilous; but - if we are prepared to act promptly - there is still one chance of escape.
No commas at all.
I was once an editor of a law review journal. I did not find Strunk helpful as to this issue. Generally, I would insert a comma after the conjunction but, for the sake of clarity, I would not place a comma before the conjunction. My wife, an English major and also a lawyer, however, disagrees with me. Of all of the grammar issues we have ever discussed, this is the only issue upon which we disagree.