Not sure what you mean - a polishing compound? They're generally just things like aluminum oxide, what you inhale during polishing is far worse than what stays on the handle.

Some friction polish kind of a deal? These are generally wax and shellac, also pretty unlikely to pose any serious danger to the user. Although, they are not going to hold up well in an item that gets washed frequently.

A rattle can or rub-on finish? Depends, but most are pretty safe when dry. I'd probably stay away from oil-based finishes, as they generally use cobalt and manganese salts as catalysts. Rattle can nitrocellulose is very safe, although probably not very durable in this use. Rattle can polyurethanes are very unlikely to pose any serious risk, although best to check the SDS first.

I think it's best to be rational about it. You're handling so many plastic items every day... if you're wary of that, that spoon is still probably not anywhere near being a top concern. If you accept that plastics are pretty safe, just stay away from a handful of formulations that are patently dangerous, but don't sweat it otherwise.

The "FDA certified" label on some casting resins is somewhat meaningless: it does not mean that a government agency looked at or approved the product; it does not mean that it is safe for your specific application; and it does not mean that a product without the label is any less safe. In fact, because the guidelines are fairly inflexible, it's quite possible for other formulations to actually be safer.