Measuring cup made of what material? If its plastic, we go back to the issue mentioned in the link house gave, about phthalates and plastic monomers possibly in your final product.
Why not mixing in a glass container? With your goggles and gloves on, put it in a tall glass container and use a long stainless steel or wood (without ink/finish) to stir in round motion. Raise speed gradually to prevent spilling and emulsions.
If your worries is lye breaking glass, it wont happen so fast. Most of the events when people have their glass breaking, I think, is because they add a lot of lye and dont mix it as they add, so a big quantity of lye sits on the bottom of the container and it generates heat and this is what breaks the glass. So add gradually while stirring well, and you shouldnt have a problem. Dont store your strong lye solutions in glass for several weeks unless its strong lab glass, and preferably work in a sink or bathtub so any spill doesnt ruin anything.