Uncle John's Soap YouTube channel has a video that says to measure your mold volume in cubic inches and multiply by 0.4 to get ounces of oil to make enough soap to fill the mold.
I used that with a 33% lye concentration in soapcalc and it was spot on.
So...if you're using 12lb of oil, or 192 oz, you can divide that by 0.4 and get 480 cubic inches. One gallon is 231 cubic inches, so that turns out to be just over 2 gallons. I would double that and use a 4 to 5 gallon stainless pot if you're hot processing. Cold process could probably be done in a clean 5 gallon bucket.
As for your stick blender and it's suitability, well, my grandmother made soap by hand and didn't have a stick blender. She would make about 5 gallons worth at a time and pour it out on a newspaper lined workbench to cure. She used a potato masher to mix it all up. So there's that. Personally, if I were working with that much, I would get one of those paint stirring sticks you put in am electric drill from Lowe's or Home Depot.