Regardless of whether you agree that using, he is indeed sexist, many contemporary readers will find it distracting and possibly downright offensive. (It’s theoretically okay to offend or even distract, but you need really good reasons.)

It is never ever okay to use he/she or him/her, and nearly never okay to use him or her or he or she. These fixes don’t fix anything because they are still distracting and worse they are lazy. The first tool to whip out when confronted with this is rewording. Many times the problem can be avoided all together:

• Delete the pronoun reference all together. E.g.: “Every manager should read the memoranda as soon as they are delivered to him [delete to him] by a mail clerk.”
• Change the pronoun to an article, such as a or the— “An author may adopt any of the following dictionaries in preparing his [replace with a] manuscript.”
• Pluralize, so that he becomes they— “A student [students] should avoid engaging in any activities that might discredit his[their] school.”
• Use the relative pronoun who — “If a student cannot use Standard English, he cannot be expected to master the nuances of the literature assigned in this course” becomes “A student who cannot use Standard English cannot be expected to master the nuances of the literature assigned in this course.”
• Repeat the noun instead of using a pronoun — “When considering a manuscript for publication, the editor should evaluate the suitability of the subject matter. In particular, he [the editor] should…”

If you are convinced that no rewording will work, you have two major options and neither is perfect.

In informal writing you can use they as if it’s singular. This will probably become widely accepted, but for now it will set some reader’s teeth on edge.

In writing that’s more formal you can use one, but it’s now rarely used outside of academic prose— it’s old and clunky.

Really, you should reword.

(Examples sentences are taken from a really wonderful usage dictionary: Garner’s Modern American Usage)