i think if you unplug it, there would be no reason to get a shock, unless it's got a battery in it. if you're that concerned about water trickling out, then the water is probably damaging the inside of the washer. i'd vote for opening it up now.
I am no tech, but i would replace your gaskets to the connection it leaks from, if it is a connection, they are pretty basic, perhaps there is the "white colored tape" (Can not recall the correct name) that wraps around and seals it?
if its one of those under $250 pressure washers, they re built to die. a somewhat busy shop might have to get a new one every year, unless you're lucky and get the magic one that lasts a lifetime. anyway, it may be nothing more then another product built cheaply... cos 80% of the people buying these things are dudes who are going to use it to clean their deck (they still haven't) or use it for one day trying to kill squirrels in the back yard (never hit one.)
Yeah, cheapies you can't fix unless it is just a washer on the water connection part.(I have had this happen more than once) More expensive commercial models all the pump and fitting parts can be overhauled.
You should have the thing plugged into a GFI (ground fault interupter) plug anyway so you don't get a shock working in a wet area.
And for fucks sake unplug it before you start to rip it apart. You can leave the water pressure on to check the source of the leak.