just so you all know, that shovel that I use to stir the ferment is metal, you are not suppose to use metal with ferment, but I kept breaking everything else or just could not get it stirred up good, went with this shovel and it works perfect....it does not stay in the bucket, it is only used for stirring...
I also keep a small bucket beside the ferment going, it is a very strong bucket,,,has a ice cream size pail of feed in it then covered with water and stirred daily,,,,if my main bucket looks like it is losing it's ferment I will put a cup or 2 of this strong stuff in with it..
on the plus size, when you stir up as much as I do of this stuff, it makes for a good arm workout
It probably doesn't make a difference since you don't leave it in.... but if you have to replace it go to a gander mountain or cabelas and check the pricing on wooden oars, or maybe even the plastic ones (though I'm not sure about the aluminum handles on the plastic ones holding up well). I have an old set of oars that would work quite well for stirring in the tub you have pictured.
Another option is the old paddles they used for making apple butter and such.... with either type of wooden paddles you could use a drill with a 'hole bit' and drill out some 1" holes to improve how it moves through the FF when mixing it.