I am thinking about equipping my large inflatable kayak with a trolling
motor to get me upriver. That way I don't need a partner.

Get a setup that properly seals the battery against water getting to it.
I'd have to imagine kayak user websites would be helpful in finding decent
setups for this. But I'd have to wonder just how much of a battery you'd
have to bring along to make it worthwhile.

What happens If I get everything wet, or it rains? Could I get killed
by electroshock?!

It would depend entirely on how large a battery you had to bring along and
how well it was stowed. If you're only talking a couple of 'motorcycle
like' gel cells then the risk is probably minimal. But if you're talking
about bringing along a larger car or golf cart sized battery then you'd want
to be careful about it.

But it all depends on how much juice it needs. You may find it's
impractical in that the size of motor needed to cover the distances desired
might require a much bigger (and HEAVIER) battery than is practical to bring
along.