Yeah, but at least you wouldn’t have to worry about being burned at the stake for being a witch. 
I’m pretty sure I know enough to build a battery. Just alternating metals in salt water. Let the local smart guys take it from there to discover which are the best metals, etc.
And with that, of course, you could make a simple telegraph. Not with machines, but just touch two wires together to cause a spark at the far end of the line.
Codes would follow as natural extensions.
Of course you’d have to invent wire, and lots of it.
And also have a need for distant communication, which wasn’t always an easy sell, except to military commanders.
Just imagine if the Marathon runner had been replaced by a telegraph - the war would have ended differently I’m sure.
Talking about dirty hands, you could explain to the doctors of the time about washing their hands carefully, and keeping wounds clean.
Actually, the Greeks were pretty good about keeping clean. It was only much later that people thought that bathing was a bad idea, and the Greeks had a pretty good understanding of proper surgical proceedures, and even did cosmetic surgeries with little loss of life or infection.
I could also invent the semaphore telegraph. It’s so simple anyone could do it, and indeed ancients had “invented” the idea but never put it into use. The French version simultaneously improved the length a signal could travel between semaphore towers and the number of “bits” transmitted per signal. A message could and did travel from one end of europe to another in a day or less.
I could also invent the hot air balloon, but that’s already been said.
Black powder would also be easy, since the three major ingredients were available at the time: you’d just have to find the right mix.
I could probably jump start differential calculus and thus give the world a head start on physics (integral calculus, otoh, I don’t remember enough to make it useful.)