just put the movement in with the date and ignore it when you're setting the time
This is the easiest and least problematic way to go. It's also how you'll find that all the JKF 2813 powered vintage watches are delivered. The alternative involves modifying the keyless works - it's not just a case of removing the date wheel.
I was going to try the modification on a couple of my JKF no-dates, but having stumbled on a post with a description/tutorial on how to make the mod many moons ago, I've since been unable to find it again. Maybe another member can recall the post - or explain how to make the mod.
It all depends on how "authentic" you want the experience of setting the watch to be. Personally, I don't really care that there's an extra click when pulling out the stem - which is why I haven't made it my life's work to find that post again.