It's not necessary to have your marriage recognised here, but it also won't hurt to do so. Your fiance needs to contact his local civil register office to find out what needs to be done.
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If you and your future spouse are both foreign nationals
You must contact the register office for foreign nationals in your future canton of residence. It is responsible for the marriage recognition procedure."
https://www.ch.ch/en/wedding-abroad/
If your husband has a B permit then you'll get the same and you can work. However, should you divorce later down the line you'd lose that dependent permit and any employer would have to go through the non-EU hiring process to apply for a new permit for you - which they may not be willing to do.
L permits which many non-EU nationals get for their employment do not allow their spouses to work without authoritisation from the Swiss authorities.