Utensils for making cold process soap should be ones that you will never use again for food. Although lye is considered a serious degreaser, wood and plastic utensils are known for absorbing chemicals and non-toxic materials. You can supply these particular utensils cheaply and easily.
Bowls: one plastic or glass bowl to measure your lye crystals into. If you are making approximately a 20 bar batch, you could use a plastic margerine-type container. Lye crystals could have a reaction with metals other than stainless steel.
For your water container, a larger sized plastic or glass container, perhaps the size of a juice jug, make sure to label it hazardous/lye water. You will need room for adding the lye crystals and for stirring.
Spoons: a large wooden is good, as it need to reach into the bottom of the pot and still give you lots of handle space to touch. You will be stirring your lye water, then your soap base, so you could use the same spoon for both. I had a large 2 1/2 foot long wooden spoon, ordered from a soap supplies shop, then I could leave the spoon in the pot and it would rest on the side of the pot without falling in. You can also use large plastic spoons as well.
For scooping your lye, try a 1/2 cup measuring cup, this works well as it has a handle for reaching inside the lye container and scooping the lye crystals.
Stainless steel pot: one large enough for both the lye water and oils to be in. Aluminum will react with the caustic base. Glass could work but you'll be heating the oils up in this pot and adding the lye-water to it later. And you'll need handles to better pour your base into a mold. Those thin stock pots work well, used those for years. But depending on the size of your batch size, any stainless steel pot will work.
Towels or blankets that you won't need anymore. The soap base is very oily and very caustic. It can bleach your towels, create large greasy oily patches, and eventually eat away at the material. I used some old but clean wool blankets and these lasted for years. You don't need to wash these everytime you use them, even if soap base is on them. That base will solidify and cure right there. After we used ours numerous times, washing these like you would clothes, with regular amounts of detergent and cold water, were not enough to get rid of the oils. You may need to wash these in hot water with double the detergent.
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utensils for making cold process soap