To use your own words, let it play out and suck it up.
While it is true that you share a computer, you invaded his privacy by opening his personal e-mail (even if it was from your sister). Had you not been nosy, you would have been totally surprised.
I get the whole not wanting a surprise birthday party because that would freak me out, too. But just imagine how your husband and sister are going to explain this one to all your guests, not to mention how it will make you look:
"I know by now you have all received your invitation to M.'s surprise birthday party. However, M. decided to read a private e-mail and found out about the party and decided she doesn't want the party. We're very sorry, but please don't come. The party is canceled."
It kinda makes you look bad.
If this were me, I'd be annoyed by the surprise party that people knew for a fact that I didn't want, but I wouldn't want to be rude and totally dump on all the hard work and planning that went into trying to create a very special and memorable moment for me.
Try to see the positive in this. And, quit reading your husband's e-mails! lol