The purpose of the respirator is to prevent you from breathing VOCs (volatile organic compounds) that are emitted by many substances in the shop.
A good example would be various paints and varnishes. When they dry/cure they release VOCs into the air, and you probably want to limit your exposure, especially if you use them in enclosed areas like a garage.

Does epoxy release VOCs? Well, epoxy cures by chemical reaction between the resin and the hardener, so there may not be a lot of VOCs involved. Various epoxies may have different properties, and MSDS (material safety data sheets) may tell you more. You can also call the maker and ask.

Having said the above...we live in a paranoid age, and if you are in the US, you live in a grotesquely litigious society.
Everybody and their brother are trying "to be safe", whether there is even a remote justification or not.

Now on to your specific case - can you smell the epoxy when it's mixed and ready to be spread over the boat? If so, consider the respirator. Keep in mind that even if you inhaled a bit of it, for a one-time casual builder, the effects will be non-existent.
OTOH, if you work with epoxy for a living, you may indeed go on the side of caution and use it even if there is no obvious need - small doses accumulated over years may damage your health.