Freezer paper is a product that has a waxed coating on only one side. It's sort of like a hybrid of oven paper (also called parchment paper, baking paper, or ladokola) and wax paper.
Neither wax paper nor oven paper can substitute for freezer paper in this particular application, because the wax on one side is being used as a temporary adhesive. After heat is applied, the paper stencil stays in place firmly enough while the bleach solution is applied, but lightly enough that it can be peeled away when you're done.
So some possible alternatives -- which I admit I haven't tried, so they are all hypothetical:
- Oven paper (or butcher paper) will work to keep the bleach solution, but will not have the same adhesive property and the stencil might move out of position while you work.
- Use contact paper -- the video you link to doesn't recommend it because it will stick right away, not allowing for repositioning, but it would stay in place.
- Use a spray adhesive to stick your oven paper down. (Make sure you look for one that's relatively weak, you don't want the paper on the shirt forever.)
- Make a substitute for freezer paper per this online tutorial: a plastic bag ironed onto regular paper.
- I wouldn't use wax paper with an iron because the wax would get on your iron, but maybe you could use a layer of wax paper under a layer of oven paper, protecting the iron but still letting the stencil stick!