If I only had one MK day, no way would I choose to do it on a Saturday. Our last trip was November, 2016 (week before Thanksgiving week). Crowds were really manageable all week. We went to MK on Saturday (before our flight home) because BTMRR is my son's favourite ride and it was just reopening after refurb. It was SOOOO much busier than any other time we have ever been there (including the Wednesday, which was our other non-party day that week, when we saw the fireworks). It took us literally twice as long to get everywhere, 10 minute waits to use the restrooms, people EVERYWHERE. I swore I would never do it again. Fast forward to our upcoming trip, and the kids have declared MK MUST be our last park, so we're going on Saturday again... but it will be our 10th park day, so we don't have high expectations.
For you, I think attending the party might be a viable option. If you show up right at 4:00, and can stay until midnight, you have almost as many hours in the park as you would during a regular party day, arriving at rope drop and leaving at 6:00. Your kids would get to see the parade and fireworks with much lower crowds, and you'd still have time to ride what you want (if that is your priority).