I'll add a caveat to what I wrote.
I said that <alarum> was trisyllabic according to Shakespeare's spelling. Certainly all dialects of English were rhotic at least up to Middle English times, and his spelling shows this.
One can hear three syllables in many Irish dialects today, and Lewis Carrol gives an example of a rhotic 'r' creating an extra syllable in 'Alice's Adventures in Wonderland where Pat, the gardener exclaims: "Sure, it's an arm, yer honour!' (He pronounces it arrum.)" - the 'r' actually gives rise to a dipthong, running from 'r' to 'u' before finishing on the consonant 'm'.
However in many dialects in Scotland the rhotic 'r' , instead of creating an extra syllable, is instead a long consonant. In attempts to indicate Scottish dialect in literature it may be spelled <arrrm> <alarrrm> etc.
Other rhotic dialects of English - as we have in Cornwall - also have a longer consonant sound than in non-rhotic dialects (RP, so-called 'Standard English', SE English dialects and so on) rather than a dipthong ...generally speaking...
Now, the point of this is - was Shakespeare attempting to indicate a rhotic 'r' giving, in effect, a discrete syllable, or did he mean by it merely a longer consonant? Likewise, what did Britten intend?
Visually, the spelling <alarum> would appear to indicate three syllables, but one can't be sure - attempts to indicate sounds accurately by using English scribal tradition and orthography is littered with ambiguous examples, and what one writer might use to indicate one thing, another writer may use to mean something quite different... and the same writer might use different spellings for the same thing from time to time, or develop a favourite spelling... or six. Shakespeare spelled his name in several different ways....
Were I an expert on English phonology I might be able to say with more precision (and possibly get it wrong... scholarship is always changing its mind - or as scholars say, 'advancing') but at least I think that outlines the problem.
Personally, I'd plump for whichever fits the music best. If it could go either way, I might toss a coin...
Incidentally, German has a highly phonemic orthography, even better after the tweaks of a couple of decades (?) ago... giving the choir the words spelled according to German orthographic convention could be a good plan.... a little time on a laptop could save a lot of time in rehearsals, maybe...
One final point - <a> in <alarum> (both of them) would be pronounced similarly to <a> in <apple> <actual> etc. (but not the rather old fashioned RP "epple" and "ectual") in some dialects... but not in others.... where it might sound more like the (current) RP <are> (where the <r> isn't actually pronounced!!)
You can end up going around in circles with English pronunciation...