If the neck doesn’t feel smooth, then it probably isn’t. I’m no expert when it comes to satin finishes, but it will definitely need sanding if it feels rough.

You have two courses of action as I see it. 1) Simply sand back until smooth (maybe P400 or P600 depending on how rough it is) and then go up the grits to P800, P1200 and P1500 etc until the feel and look is how you want it to be or 2) sand back until smooth and then spray one thin coat of satin clear on as the final coat. If when dry, that still doesn't feel right or smooth enough, then you'll probably have to revert to method 1. It will depend on how well your can of satin clear sprays as to how smooth the finish will feel.

You aren't trying to put a shine on it, so you don't have to wait for the finish to harden too much before sanding back, maybe a couple of days rather than a couple of weeks.