Good lateral thinking but
Fisrt, you go forward to get a towel
Second, you go aft to get a bucket and line out of the lazarette, assuming the galley sink is not accessible or the pressure water not on
Third, towel overboard in bucket
Fourth, return to galley...
Even if you grab a wet towel from the settee you're giving the fire too much time. A fire's size doubles every 30 seconds and if it is behind the stove, etc., you don't want to start looking and thinking.
There really are fire blankets, they are not expensive. Aramid or kevlar, yes, pricey, plain old cheap tight wool blanket will do equally well. It really should be in a box, wall mounted and ready to pull and use, if you plan to use it. The extinguisher allows you to keep a little further back from the flames though, so it might still be worth the mess.