How to use knife tool without connecting to other edges

I’m trying to make a broken mirror, but I’m struggling with some parts because when I cut the line I need with the knife, it connects to another edge I don’t want it to.

An example of what I’m trying to cut:

But this is what happens:

I don’t want this edge, but when I dissolve it, it messes with other edges

Is it possible to do this?

The knife edge (start point) will have to connect to some existing edge.

These are done to protect from concave ngons, which sort of don’t work. I assume your end goal here is to do some insetting or something to make the break, just ignore the extra edge when doing so and it’ll be fine, the end viewer will never see it.