I want to mix the two chemicals to get a solution that doesn't stratify, and does not require constant shaking (mixing) during use.

Mixing oils and alcohols doesn't always go so well. You can try using pure ethanol, not a water mix. You may also get some luck if you homogenize it, like they do with milk, sometimes a high speed mixer, say several thousand RPMs, will work instead of the big bulky equipment. Depending on what you're using it for, adding certain lyes or soaps will often reduce the cohesion of the chemicals to allow them to mix.