How can I handle black pepper without sneezing?

Your local hardware store or DIY shop will likely have an assortment of dust masks you could try. The simplest ones would be cheap and very quick to put on and remove, and should help.

It seems a little over the top to have to put on a mask for using pepper, but perhaps you're extra sensitive and it's just something you'll have to deal with.

Do you have any reaction at all from eating things with lots of black pepper?

Finally, you might look at how you're physically dispensing the pepper. If you're shaking it from a container you're likely to stir up a small cloud of fine pepper dust. If you're not already doing so, consider trying to use a tiny measuring spoon or even the wrong end of a regular spoon to scoop a little pepper out of the container directly and add it to your food--less sprinkling/shaking, less irritant in the air.

I guess you are using already grounded pepper. If you mill your own, I think the resulting particles are too big to fly their way to your nose!

Edit

Answering your comment: So I think you could prepare something like Black Pepper Oil (adapting the recipe for grounded pepper, just filtering the resulting oil with care) and suffer your sneezing much less often.

I think any type of mask/plugs that would stop the pepper dust getting in your nose would work. Perhaps a surgical mask, or a painter's dust mask would help. Swimmer's nose plugs are another option.

My dad makes horseradish fresh every year for Passover, and he actually uses a full military issue gas mask to keep the fumes up. In his defence, the stuff will bring an adult to tears at twenty paces.