No, there won't be an option to not use a psychotrigger. He will offer you quite a few different psychotriggers to choose from: a clicker, feather to nose, grip sear, tab sear, etc. Having a non-anticipatory psychotrigger is an integral part of his system. The reason is that if you know when the arrow will be released, your body will have pre-ignition reactions, similar to flinching when you shoot a gun: flinching is inevitable; whether you flinch, before or after the bullet leaves the gun is something you can control. Besides pre-ignition reactions, the psychotrigger is a key factor in controlling target panic. Joel defines two types of systems: open loop and closed loop. You have to understand these and why a closed loop system is necessary to control target panic. Under Joel's system, after everything else has been said and done, and the only thing left to do is release the arrow, there is a tiny movement you need to make to trigger the release. Learning to focus on this movement, to the exclusion of everything else in the universe, and being able to control and stop it if necessary, is the key to avoiding target panic and pre-ignition reactions in Joel's system.
There are certainly other systems out there other than Joel's system, but I can't imagine Joel's system without a psychotrigger.