The use of the pronoun “he” as a bound pronoun of neutral gender is problematic on two grounds. First, its use is blatantly sexist (although the sexism is of a historical nature, so that those who continue to use “he” in this way have a defensible position). Second, and more importantly, many readers confronted with such a use of “he”, including myself, tend to find that it causes a jarring effect as they stop to wonder whether or not the writer intended to imply that the referent of the pronoun is male. Anything that causes a jarring effect like this on a substantial portion of your readers should be avoided, as it serves only to distract them from the important substance of your writing.
Now, I turn to a more recent variant of the same problem. The use of the pronoun “she” as a bound pronoun of neutral gender is problematic on two grounds. First, its use is blatantly sexist (although the sexism is of an anti-historical nature, so that those who continue to use “she” in this way have a defensible position). Second, and more importantly, many readers confronted with such a use of “she”, including myself, tend to find that it causes a jarring effect as they stop to wonder whether or not the writer intended to imply that the referent of the pronoun is female. Anything that causes a jarring effect like this on a substantial portion of your readers should be avoided, as it serves only to distract them from the important substance of your writing.
But what alternatives are there? In everyday speech, “they” or “them” is used for this purpose, but this disturbs the sensibilities of prescriptivists, who, I should remind you, are a substantial portion of your readers. And anything that causes a jarring effect like this on a substantial portion of your readers….
Rewriting the sentence is the only practicable alternative. Do it and be done with it.