Traveling to Cancun through Zurich as the non-EU spouse of an EU citizen

While I don't have any personal experience with this particular scenario, you probably don't need a visa because as a permanent resident in a Schengen country, you can travel to other Schengen countries for three months in any six-month period (and Switzerland is part of the Schengen area, even if it's not a full member of the EU). This is completely independent from the fact that your husband is Italian. Make sure to have the relevant residence permit with you (and a valid passport but since you are going to Cancun, I assume you will have one with you in any case).

One caveat is that you only said you are “living” in Italy. Are you a permanent resident there? Does your husband live there with you? Traveling with your husband or having a residence permit mentioning the fact that you are the relative of a EU citizen is sometimes required to travel in the EU without visa (albeit not in the Schengen area itself where, per the rule cited above, a regular residence permit alone is enough). If you want to be absolutely sure, you could contact the Swiss consulate for your region and ask them directly.

If the previous conditions do not apply, getting a visa as the spouse of an EU citizen should be quicker, easier (e.g. no health insurance or bank statement should be required) and, importantly, not cost you anything.

Source: Travel documents for non-EU family member on the EU general website.

If all fails, the EU could also offer some assistance. You could probably also use the first option (“Quiero saber más sobre mis derechos según la normativa de la UE en la situación en la que estoy”/“I want to know more about my rights under EU law in a situation I am currently facing”) and ask the same question there.

PS: Note that rules regarding “airport transit visa” do not apply for this travel as you will be leaving the international zone of the airport and entering the Schengen area in Zurich. If you had no residence permit, you would need a full Schengen visa and could not rely on the transit exemption or apply for a transit visa.

No. Assuming you have a permit for Italy - or any Schengen country for that matter - you do not need any visa. So long as you're not staying for longer than three months, you don't need any visa for Switzerland.

Me (EU citizen) and my Israeli partner (who has a permit for an EU country) have used (the Swiss sector of) Basel airport to fly to within and outside the EU on multiple occasions, and we have never run into any visa issues. Residence permits issued by Schengen countries allow the holder of said permit to freely visit every Schengen country for up to 3 months each 6-month period. Switzerland is a Schengen country.

One note is that the Swiss are keen on checking (non)declared goods. Upon entering Swiss territory (also by car or rail) you might be subject to a border control. If you are carrying certain goods, they must be declared (and pay taxes). But if you are taking normal travel items, there is no need to worry.