In this example, it should definitely be who.
A single word question like that is typically seen, grammatically, as an ellipsis for a full-sentence version, as you say. But elided words/phrases are almost always things which have already just been said, so following “He ate the entire cake,” the natural ellipsis would be “Who [ate the entire cake]?”, not “Whom [are you talking about]?”.
Even in cases where it would make formal sense, though, “Whom?” is rarely used alone:
The tiger ate him up entirely!
Who?
“Whom did the tiger eat?” or “Ate whom?” sound fine to my ear (as do their equivalents with “who”), but “Whom?” alone sounds quite stiltedly pedantic. As ShreevatsaR has described very well, whom is — while not obsolete yet — certainly of limited use, and when in doubt, who is pretty much always an acceptable alternative nowadays, and is often more idiomatic.
The Wikipedia link about the accusative case explains that
Modern English, which almost entirely lacks declension in its nouns,
does not have an explicitly marked accusative case even in the
pronouns. Such forms as whom, them, and her derive rather from the old
Germanic dative forms, of which the -m and -r endings are
characteristic.
Now, whether to use who or whom in your sentence entirely depends on which case should be used, accusative (whom) or nominative (who).
In English, it is grammatically correct to use nominative after the verb to be as in
It's he who stole my car. It's they who told me the truth. It's she
who lied to me.
However, we know that "It's me" (using the accusative case after to be) is broadly used in English. But it is just a few exceptions.
In your sentence, it is appropriate to use the nominative case as it is the complement of to be. If you divide the sentence into two parts:
He must decide / He should be who => He must ask who he should be => He must decide who to be.
in the same way as:
He must decide / He should meet whom => He must decide whom he should meet => He must decide whom to meet.
He must ask / She is who => He must ask who she is. (This question cannot be shortened with wh-word + to-infinitive as the subjects are not same.)
We don't ask,
*Whom is he? or *Who is him?
*Whom am I? or *Who am me?
because whom and him/me are the accusative case and can't be a complement of the verb be in this case.
Note: "He must decide who he wants to be" is more idiomatic than "he must decide who to be".
Best Answer
Whilst there are some posts to a question here that deal with some aspects of the usage of whom, none of them address the issue arising from the Original Poster's question here.
Many posters on ELU (this site) write about the death of whom in natural English. The death of whom, however has been over-exaggerated. Many of the writers foretelling the demise of whom advise using who in all instances or reformulating the sentences in which it occurs. However, these writers advising the avoidance of whom are meting out the same prescriptivist advice that right-minded descriptive grammarians abhor. This advice in fact can be positively damaging because in the modern grammar we often actually have to use whom instead of who to make our sentences grammatical.
The most important of these situations is when who/m is the object of a preposition in a relative clause construction. In such situations, who is often quite straightforwardly unusable. The following, using who, are all ungrammatical:
Contrastingly, the following are all fine:
Now, some writers might argue that these sentences should be reformulated so as to avoid the use of whom. However, this is complete piffle. To do so would be merely to pander to the personal predilections and prejudices of certain writers. It would have nothing to do with either grammar or good style. The only reason to suggest reformulating these sentences would only be so that the personal predilections of such writers held true.
Here is why these sentences shouldn't be reformulated. In each case the consideration is one of information packaging. Information packaging is merely about how we present new and given information to achieve the emphasis we want and to make our sentences easier to process.
In the first example, the formulation of the sentence requires contrastive stress on whom making the sentence more emphatic - this would be lost in a reformulation. This stress ties the second clause in more tightly to the first. In addition, the sentence construction builds up the readers anticipation as the sentences progresses, rendering the focus of the sentence - the injuries - more potent.
In the second example, if reformulated into two sentences, the first would become quite redundant:
The second sentence in the reformulated example, also lacks the focus of the original. The original puts the emphatic nothing at all in the focal position right at the end of the sentence. The reformulation puts about her at the end. Hardly the same effect.
In the third example, I cannot really see how a viable reformulation would work. Whichever way it was done, it would lose its emphasis:
As can be seen the reformulation above puts the emphasis on harming us as opposed to deserve better.
The Original Poster's Question
The question of which of the two formulations is best in this instance is mute. It depends entirely on the context of the sentences and the objectives of the writer. However, in terms of the grammar I sent emails to four others, one of whom responded is clearly grammatically correct. I sent emails to four others, one of who responded is clearly ungrammatical.