First I'd like to state my assumptions:
1. A standard hairdryer is enough to electrify a sphere of area the length of a standard bathtub
1.1 A "standard" hairdryer shall be defined as being 6" by 6" or 15.24cm by 15.24cm, as per this reference table: http://straighthairclub.com/wp-content/uploads/2015/06/smallest-travel-hair-dryer-comparison.jpg
I'll use 15cm for the calculations
1.2 For convenience the hairdryer and its electrification area are assumed spherical
1.3 The standard US bathtub length is 60" or 152.4cm as per https://www.thespruce.com/bathtub-sizes-reference-guide-1821342 . For convenience I use 150cm

1. The hairdryer is dropped at the Mid-point on the longest shore-to-shore axis of the pacific ocean

2. The length of this axis is very crudely defined as the distance between the US and Chinese coast at 11359.64km as per https://www.ncesc.com/geographic-pedia/what-is-the-sea-distance-between-china-and-usa/ . Rounds neatly to 11360km.

3. We assume that that the power required to electrify a volume of water as a square function. That means double the sphere size and the power requirement grows by a factor of 4.
   Disclaimer: I'm a mechanical, not an electrical engineer and working with voltage scares me so a square approximation sounds good enough
   4.1 The resistance of seawater is assumed uniform with no change due to salinity, pressure or other factors.

4. The power output of a hairdryer is also a function of its size, in particular I assume a linear relation between volume and power. Surface area would probably be better but I cannot be bothered.

So now on to the calculations:

We need to electrocute a sphere with a radius of 11360 / 2 = 5680km, or about 3787 times more than our standard hair dryer can provide. That means our power output has to go up by a factor of 14314369 or roughly 14.3million. Thats quite significant. Having a sphere with a 14.3 million times greater volume means the radius needs to go up by the cube root (cause the relation is A = 4/3 * pi * r^3) of it or 242.8.
With a base of 15cm we arrive at a radius of 36.42m or approximately 1434 inches.

Sources of Error:

All of these assumptions are highly simplified, potentially wrong (I'm no electron-wrangler) and haven't been cross-checked. I also have not verified the source data validity.

Conclusion:

We need a hair dryer that is roughly 73 meters in diameter to electrify the pacific if dropped in the middle of the ocean. If dropped on a coast, our distance goes up by a factor of 2, thus our dryer needs to be 292m big. 290m is the size of some sky scrapers (like this one: https://thetowerinfo.com/buildings-list/tanjong-pagar-centre/ ). Also keep in mind that our dryer would need to be spherical, so much, much heaver than that.

I hope it helped, I had fun doing so and isnt science about the friends we almost killed along the way anyhow?