One concern I have about visiting Crimea is whether I can receive consular assistance. The Australian government does not recognise Russia's control of Crimea, and that limits the ability of it to provide consular assistance. I don't have citizenship or permanent residency in any other country.

I don't usually think about whether I need consular assistance, but the state of rule of law in Russia means I'm more concerned about it than for other countries I visit.

Are there any alternatives for consular assistance, such as a third-party country (perhaps Switzerland?) providing consular assistance?

Consular assistance in Crimea itself will be limited; as such you should head for mainland Russia and contact the Australian embassy in Moscow in case of any issues.

That said, Crimea is no longer particularly unsafe, no matter what some governments keep saying (mostly out of disapproval at the fact that Crimea is now part of Russia) and if you stick to common sense and the usual precautions, you should have an enjoyable trip.

In particular, if you follow the laws, getting arrested by corrupt officials and extorted isn't an issue for tourists in the area.

Remember the following:

1. Crimea is only accessible by domestic flights from elsewhere in Russia, or by the Kerch ferry




2. Logically, then, you need to apply for a Russian visa to get there - Ukrainian ones aren't valid.

From the first page that you should look to, your goverments consular advice:

Crimea, do not travel

We advise against all travel here due to the very high risk. If you do travel, you should typically seek professional security advice. Be aware that regular travel insurance policies will be void and that the Australian Government is unlikely to be able to provide consular assistance.

(Emphasis mine, but basically I would like to highlight all of that text.)
As you say the problem of providing consular assistance stems from the fact that Crimea is not recognized as Russian territory by Australia. The same holds for any other UN member nation, except Afghanistan, Cuba, Kyrgyzstan, Nicaragua, North Korea, Syria and Venezuela. Now I'm not sure how friendly your government is with the Nicaraguans, but I find it unlikely that the North Koreans will issue you a temporary passport should you loose yours at the beach. Note that the Smarttraveller advice for Crimea is:

If you are unable to leave, avoid demonstrations and large public gatherings.

And even within Ukraine your consulate would only issue documents for emergency travel to your embassy in Warsaw:

Australia has an Embassy in Kyiv, as well as a Consulate, headed by an Honorary Consul. The Consulate should be approached in the first instance for all routine consular enquiries. The Australian Embassy in Warsaw manages passport matters for the Consulate in Kyiv. The Consulate in Kyiv is able to issue Provisional Travel Documents for emergency travel to our Embassy in Warsaw, and is able to receive passport renewal applications and send them to Warsaw for processing (the wait time can be several weeks). The Consulate does not issue Australian passports.

If @Doc in his +1ed comments and this has not convinced you yet, let me summarize:

Do not count on any consular assistance available to you.

If you are concerned about access to consular assistance, it is a stupid idea to consider travel to Crimea at this moment, given especially that you have previously demonstrated being of the more risk-averse type, being concerned about alcohol exclusions in your travel insurance policy and lack of manhole covers in Mongolia. Be aware that no standard travel insurance policy will cover Crimea at this moment.