Very few of the of style guides I consulted offer advice on punctuating words intended to be read phonetically letter by letter.
From The Chicago Manual of Style, sixteenth edition (2010):
6.77 Hyphens as separators. A hyphen is used to separate numbers that are not inclusive such as telephone, social security numbers, and ISBNs. ... It is also used to separate letters when a word is spelled out letter by letter, in dialogue, in reference to American Sign Language, and elsewhere.
[Relevant examples:]
"My name is Phyllis; that's p-h-y-l-l-i-s."
A proficient signer can fingerspell C-O-L-O-R-A-D-O in less than two seconds.
So Chicago is firm on the hyphens but flimsy on uppercase versus lowercase letters.
Webster's Standard American Style Manual (1985) goes all-in for lowercase:
4. Hyphens indicate a word spelled out letter by letter.
p-r-o-b-a-t-i-o-n
But The Oxford Guide to Style (2002)—which doesn't address the question of how to represent a word that is being spelled out letter by letter—offers advice on a related question that indicates why a lowercase treatment is potentially problematic:
Use hyphens to indicate stammering, paused, or intermittent speech:
[Relevant example:]
The bell went r-r-r-r-r-i-n-g-g! and then fell silent.
Of course, if Oxford's example had used all caps instead of lowercase, the situation would be just as potentially problematic (but louder):
The bell went R-R-R-R-R-I-N-G-G! and then fell silent.
In many instances, however, loudness is not a factor:
Are you saying r-a-i-s-e or r-a-z-e?
And in those instances I see a minor advantage in avoiding the drawl interpretation by using all caps:
Are you saying R-A-I-S-E or R-A-Z-E?
An alternative (used on the record cover for Tammy Wynette's classic song "D.I.V.O.R.C.E." shown at 0:02) is to replace the hyphens with periods. To my eyes, capital letters separated by periods look less odd than lowercase letters separated by periods. I notice, however, that whoever transcribed the lyrics for that YouTube posting consistently used all caps and hyphens to spell out the words that Tammy and her ex-mate don't want little J-O-E to understand. This choice is evidently quite common, although it is by no means universal, as the split examples in Chicago indicate.