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What launcher are you using? With Nova you can set up your own shortcuts through Activities. Depending on your camera app, you might even get it to go straight to recording.
I'll check to see if I can find an app that does what you want.
Found a bunch but most of them seem to record through their own cams, not using your phones default camera.
If you can spare two presses, then something like mashcord might suit you.
https://play.google.com/store/apps/details?id=com.paclab.mashcord
If you still want an app that records with one press (through their app) just search the store for fastcam and a bunch of results will show up.