Check the Wide Open schedule for when the courses will be available that weekend:http://www.kcwideopen.com/index.asp
WyCo in Bonner Springs will be open all weekend along with Prairie Center in Olathe. Both are only 20 or 30 minutes west of downtown KC between KC and Lawrence. Lawrence has Centenial Park and Clinton Lake too. I don't think you'll have any trouble playing some quality disc golf in KC even with the KC Wide Open going on.
Of course most of the time the Wide Open is happening you'll be at Wakarusa anyway I expect. Don't get away from the area without playing Water Works is all I can say.