Well I guess I'm glad to know I'm not the only one, but it's not something to be "glad" about, as it's still a mild inconvenience for us.
The idea proposed by Douglas, regarding using a mask and nitrile gloves, as well as the advise of taking a benadryl or perhaps another antihystamine seems like it would solve the problem, or at least lessen it. As hayday said, it's not a major inconvenience but still.
I guess now the question is what is causing this? What is the science behind this? Is it indeed the terpenes in the air? The live resin? Both? Now that I think about it, I don't think my idea of doing a dry trim will help either, because in the past when I've received untrimmed bud and had to trim it myself, I'd also get sneezy and itchy, but luckily it wasn't as intense as when wet trimming, when the whole vicinity smells incredibly loud.