Personally, I don't think "s/he" is very elegant (see also this post on ELU from before the discussion on Meta started). I don't object to using singular they, so for me it's easy to use that.
From your perspective with stylistic choices in mind, I would try to avoid them both. I've stated a few examples at the end of my answer which show that it's quite easy to avoid having to use pronouns all together.
The FAQ on pronoun use on the SE network may be found on the main meta site.
On the use of he/she as opposed to they, the FAQ says:
5. "Gender-neutral"? Does that mean like "he/she"?
Not quite. While “he/she” and similar compound pronouns are better than a default masculine “he” alone, gender-neutral writing works to avoid gendered terms entirely when gender is unknown, either through rephrasing statements to avoid pronouns or through the usage of singular (or plural) “they”. For examples and other methods, see Kate Gregory’s answer to a related question - Define "gender-neutral language"? (CoC FAQ)
In that sense, he/she and s/he are considered less inclusive than they. Based on comments from community moderator Catija on the main Meta site, the preference for gender neutral language extends to hypothetical people:
A post speaks of a hypothetical or generic person. In this case, unless the gender somehow matters to the post, being gender neutral is beneficial.
Avoiding pronoun disputes in practice
In your example, however, you could simply write in the plural form. The subject would then be those candidates who want to win an office to prevent its role from being done (which is a simple rewrite of the question title). Your sentence could then be:
Such candidates are not intending to omit doing the job they are elected to do; they merely choose to follow a particular policy.
In this case you use plural they, which is perfectly gender neutral and avoid the objection to using it in the singular form.
Another approach would be to turn the sentence around:
Merely following a particular policy is not the same as omitting to do one's job.
Such rewrites are also encouraged by the FAQ:
4. I find it really distressing to use pronouns in a way I think is wrong. Is there really no alternative?
You can often avoid using pronouns altogether. It's actually pretty rare to need third-person pronouns at all on most Stack Exchange sites. But conspicuously avoiding using pronouns for one group of people while using them normally for others is a way of refusing to recognize their identity, and that is discriminatory. Please don’t do that.