If there is leakage from the shore power into the water near the boat, the outdrive is in the water so anything connected to the outdrive, an ungrounded gimbal housing, could have that voltage waiting for a path to ground.
You could receive a shock if you touch the gimbal housing (if unbonded to ground) and another metal part with a path to the shore power system ground. If that is happening, you could prevent the tingling by bonding the outdrive and gimbal to ground, which it should be anyway.
But that does not solve the bigger problem, the shore power fault, if that is the source of the tingling which is the current flowing through your body to ground. AC is more likely to be felt than DC, and is much more dangerous. I boated in an area where drowning fatalities to swimmers resulted from shore power leakage current flowing through the water. That is why most marinas do not permit swimming.
If it appears that there may be leakage into the water, this should be reported to the marina checked out by a competent electrician. (There is a good article on this in the latest Boat US magazine by the way.)